Sequence & Series 04 | A.G.P. & H.P. | CLASS 11 | JEE | PACE SERIES

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  • Опубліковано 9 лис 2024

КОМЕНТАРІ • 1,7 тис.

  • @tanishq2957
    @tanishq2957 3 роки тому +109

    1:38 - Start of A.G.P.
    28:47 - Start of H.P.

  • @neelanshupanigrahi2553
    @neelanshupanigrahi2553 3 роки тому +487

    yes we want a session on The Golden Ratio

    • @yashsahu3187
      @yashsahu3187 3 роки тому +4

      Yes sir we want a video on golden ratio

    • @metawhirl4609
      @metawhirl4609 3 роки тому +7

      Fibonacci sequence you want huh

    • @solenoid6545
      @solenoid6545 3 роки тому +2

      @@metawhirl4609 computer m bhi aata h isliye. Hm sb ne optional m CSc liya h

    • @kgamer4800
      @kgamer4800 2 роки тому +2

      The golden ratio is 1.618

    • @tirthmodi9294
      @tirthmodi9294 2 роки тому +1

      @@solenoid6545 root 5-1/2

  • @himstitute9030
    @himstitute9030 3 роки тому +144

    areey now I got remember where I listened the word "GOLDEN RATIO" last time..In the movie "Super 30" "tmhare chehare pe par feee nhi hai 😂😂" Sir now I definitely want a lecture on it

    • @its_yash9360
      @its_yash9360 3 роки тому +1

      Yess you are right.

    • @IshaansGoodLife
      @IshaansGoodLife 3 роки тому +1

      ua-cam.com/video/xm40afLBNXw/v-deo.html ye dekho bhai🤣

    • @neelanshupanigrahi2553
      @neelanshupanigrahi2553 3 роки тому +1

      @@IshaansGoodLife sahi hai bhai
      par babita is missing

    • @Jasbirkaurgill22
      @Jasbirkaurgill22 3 роки тому

      Sir to kho gye 😭😭😭

    • @HARSHG1243
      @HARSHG1243 3 роки тому

      @@Jasbirkaurgill22 new channel hai unka BHANAT MATHS

  • @neutron417
    @neutron417 3 роки тому +299

    We want golden ratio lecture... that is much needed

  • @arnawbaitha8748
    @arnawbaitha8748 3 роки тому +98

    Sir, We need a video on Golden Ratio

  • @pawanbishnoi4886
    @pawanbishnoi4886 3 роки тому +27

    Answer of hw qtn - 4 sq. units.
    [It was an decreasing infinite GP (2, 1, 0.5,..) whose sum is 4]

    • @Durgaprasad_Nayak
      @Durgaprasad_Nayak 2 роки тому +3

      Sathik 😀😀

    • @arachnix9335
      @arachnix9335 Рік тому +2

      Thank you stranger, I was solving it and ended up finding the sum of the sides only, your comment made me recheck my solution and fix it accordingly. Thank you. So glad that this community is so helpful.

  • @ashusaklani
    @ashusaklani 3 роки тому +56

    Ye sir we want lecture on Golden ratio😍
    Thank you for each and every thing you are doing for us🙏🏻

  • @tosifsayyad75
    @tosifsayyad75 3 роки тому +57

    Yes sir we want a lecture on Golden ratio.

  • @AdityaKumar-rt2qf
    @AdityaKumar-rt2qf 3 роки тому +205

    Yes we want a lecture on golden ratio

  • @doyamvashishtha9642
    @doyamvashishtha9642 2 роки тому +24

    Yes we want to understand everything about golden ratio😊

  • @nikitathakur7647
    @nikitathakur7647 3 роки тому +64

    41:39 Sure Sir 😄
    Pls syllabus completion k baad *Golden Ratio* par lecture...
    Ab toh curiosity bani rahegi lecture k liye 😁😅😅

  • @cube7353
    @cube7353 2 роки тому +30

    Hey friends,
    We can use the formula
    (a / 1-r ) + dr/(1-r)² for infinite agp also. Hope it helps!

    • @avinash703
      @avinash703 2 роки тому

      Thanks

    • @cube7353
      @cube7353 2 роки тому +1

      @@avinash703 :D

    • @abdulkhadarainur4348
      @abdulkhadarainur4348 Рік тому +1

      That doesn't work quite right when first term is a multiple of r. And even after taking r common, it fails in a few situations.

  • @kjsdhaliwal4347
    @kjsdhaliwal4347 3 роки тому +138

    Yes sir hame golden ratio ka lecture chahiye

  • @lifefact2182
    @lifefact2182 3 роки тому +3

    45:00 ans of hw --> 4unit square

  • @SahilZen42
    @SahilZen42 Рік тому +2

    We can easily calculate the area of first sqaure which is 2 unit square.
    Imagine all the squares are shrinking down to its half value infinitum...
    2 + 1 + 1/2 + 1/4 + 1/8 + ••• + 1/∞
    =2 + 1 + 1= 4 Ans.
    Think this problem geometrically👍

  • @DK34777
    @DK34777 3 роки тому +3

    अलख sir हमेशा बच्चों का भला सोचते हैंइसलिए ज्यादा से ज्यादा फिजिक्स वाला ऐप को सपोर्ट कीजिए🙏🙏🙏

  • @horridakhil123
    @horridakhil123 3 роки тому +28

    ""Aaloo Sade Sade , tamatar gale gale ,sir aapne hame titar bana diya , rajai me pade pade ""❣️❣️ And plz tell us more about golden ratio ((blessing from Dehradun))

    • @ashanihalani9079
      @ashanihalani9079 3 роки тому

      Sir pls teach us about the golden ratio

    • @cameraman810
      @cameraman810 2 місяці тому

      Reply me kya kar rha hai bhai comment karna

  • @mohd_faizan
    @mohd_faizan 3 роки тому +13

    Ans of last ques
    Sum of all the areas of all the squares = 4 unit ²

    • @aishanshuike882
      @aishanshuike882 3 роки тому +1

      Bro can u tell how u find it

    • @tanishrashm3645
      @tanishrashm3645 3 роки тому +4

      @@aishanshuike882 Diagonal of square is equal to Diameter of circle , if square is inscribed in circle ...equate them , u will get A1 = 2
      A2 = 1
      A3 = 1/2
      A4 = 1/4 and so on ....
      These terms are in Infinite GP

    • @aishanshuike882
      @aishanshuike882 3 роки тому +1

      I got that bro before itself , then too thanks for reply

  • @anjaleegusain8136
    @anjaleegusain8136 3 роки тому +3

    According to me the answer of homewo question is 4
    As the areas of square are in G.P with common ratio 1/2

  • @shivamarora2969
    @shivamarora2969 3 роки тому +22

    41:30
    Yes sir, please make a video on golden ratio whenever your schedule allows.

    • @adii18s
      @adii18s 3 роки тому +1

      Your how much syllabus completed of class 11 for jee??

    • @shivamarora2969
      @shivamarora2969 3 роки тому +1

      @@adii18s very less 30-40%

  • @thegauravschannel7397
    @thegauravschannel7397 3 роки тому +9

    Good Morning/Afternoon/Evening whenever you are watching this....
    Sir please provide us the lectures on left portions of Trigonometry.....🤗🤗
    Also please tell us about the sum of HP, supposition of terms in HP, relationship between AM/GM/HM.... 🤗🤗🤗And how to find AM/GM/HM of more than two terms...🤗🤗🤗🤗
    Also a special lecture on logarithms.... ✍🏻✍🏻✍🏻✍🏻✍🏻
    Cordially Thanks for your precious teaching 🔥

  • @sajalshrivastava6227
    @sajalshrivastava6227 3 роки тому +32

    Sir please launch JEE 2022 batch after March so that we can start our prepration early.
    Edit :- Sir maths ke liye Aman Sir is the bestest.
    2nd Edit :- I don't think that it is possible to get Aman Sir as our Maths teacher in JEE 2022 batch but I think something big is gonna to be happens.

  • @hitanshramtani9076
    @hitanshramtani9076 3 роки тому

    sir sum of infinity in agp ======>> a/1-r + (rd)/(1-r)^2 timming 23:00

  • @maulikjain2259
    @maulikjain2259 3 роки тому +4

    Ans of H.W. is :-
    The required series is 2, 1, ½_ _ _ _ _.
    Sum of areas of infinite squares = 4 sq. units

  • @sonupaswan9099
    @sonupaswan9099 3 роки тому +4

    Golden Ratio is 1:1.26...🙏🙏🙏

  • @Rimmee15
    @Rimmee15 3 роки тому +8

    When you finally get something good, enjoy it. Don't always go looking for something better...❤️👍🌺🌱

    • @Lucifer-pj8vc
      @Lucifer-pj8vc 3 роки тому +1

      Aapke itne saare subscribers hai😯😯

    • @darakhshayasmeen
      @darakhshayasmeen 3 роки тому +4

      @@Lucifer-pj8vc ha yrr 😜😜😜😜
      Nice observation!!
      Dp ki vajah se syd 🤣🤣🤣

    • @flipperxprem998
      @flipperxprem998 3 роки тому +1

      TQ very much ❤️

    • @Lucifer-pj8vc
      @Lucifer-pj8vc 3 роки тому +1

      @@darakhshayasmeen Nhi mai to waise hi 😅 information ke liye 😁

  • @aryankr8608
    @aryankr8608 3 роки тому

    Sir answer of homework question is 4 unit sq. The series of decreasing area of square is 2,1,1/2,1/4,.........

  • @darakhshayasmeen
    @darakhshayasmeen 3 роки тому +21

    33:49
    Ap bole to arithmetic progression
    Alakh Pandey mt samajhna
    🤣🤣🤣🤣🤣🤣😜😜😜😜😜

  • @vijaypalgangwar6155
    @vijaypalgangwar6155 2 місяці тому

    00:00: Introduction to sequences and series, focusing on Arithmetic (A.P.), Geometric (G.P.), and Harmonic Progressions (H.P.).
    04:30: Explanation of Geometric Progression (G.P.) and how to identify its terms through examples.
    11:15: Discussing the concept of Arithmetic-Geometric Progression (A.G.P.) and its formation by combining A.P. and G.P.
    20:45: Detailed breakdown of how to derive the sum of terms in A.G.P. using formulas.
    30:10: Introduction to Harmonic Progression (H.P.) and its relationship with A.P. through reciprocal terms.
    38:20: Insight into deriving the sum of terms in H.P. and the significance of finding reciprocals.
    44:00: Summary of the session emphasizing the importance of understanding various progressions for JEE preparation.

  • @Piankamoniga
    @Piankamoniga 3 роки тому +34

    0:25 "kaise hai aap log" in carryminati style 😂😂

  • @ankitadangi1655
    @ankitadangi1655 3 роки тому +1

    Sir samj m a rha hai achhe se.....ek dam bhannnnnnaaatt pdayi chl rhi h.

  • @yesh_grg
    @yesh_grg 3 роки тому +24

    The man who is recording lecture on his leave
    Thanku sir❤
    Thoda rasayan leela wale sir ko bhi boldo woh bbi extra class lele

    • @pranjaltiwari1788
      @pranjaltiwari1788 3 роки тому +1

      Bro wo bhi daily aate hai

    • @yesh_grg
      @yesh_grg 3 роки тому

      @@pranjaltiwari1788 kaash

    • @pranjaltiwari1788
      @pranjaltiwari1788 3 роки тому

      @@yesh_grg wo srf kal nhi aayr the otherwise roz aate hain

    • @adii18s
      @adii18s 3 роки тому

      @@pranjaltiwari1788 Your how much syllabus completed of class 11 for jee??

    • @adii18s
      @adii18s 3 роки тому

      @@yesh_grg Your how much syllabus completed of class 11 for jee??

  • @ShantanuHippargekar
    @ShantanuHippargekar 3 роки тому +5

    Really we all miss you on this PW Platform

  • @anuverma23498
    @anuverma23498 3 роки тому +7

    Sir aapki entry ek dam BHANNAT hoti hai....Maza aa gaya....Video ki starting mein hi maza aa jata hai ki video ko band karne ka mann nahi karta...Thank you Alakh sir and team🙏🤗

  • @anjaleegusain8136
    @anjaleegusain8136 3 роки тому +7

    Jai hind sir
    Sir we want lecture on Golden ratio after our syllabus is completed
    as it's name has golden.. 😍

  • @A4vinish
    @A4vinish 3 роки тому +23

    S sr we want golden ratio
    Silver, platinum , daimond bhi hoga is math ki maya m janaa h hmko apke sath 🤤👍

    • @adii18s
      @adii18s 3 роки тому +1

      Your how much syllabus completed of class 11 for jee??

    • @anonymous_magnus
      @anonymous_magnus 3 роки тому +1

      @@adii18s create a group for discussion 😄

  • @umangmathur9301
    @umangmathur9301 3 роки тому

    46:20 -- SIR HW. QUESTION ANSWER IS---: 4
    Bcz, the resulting sequence will be:-- 2 + 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +...................+Infinity
    hence, 2+[ 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +...................+Infinity]
    The Sequence in the Brackets is the Sum of Infinity G.P. With Common Ratio = 1/2
    hence
    as |r| < 1,
    We can use S= a / 1-r
    --- S = 2+[1 / 1-(1/2)]
    ----S = 2+2
    ----S = 4 Answer

  • @nehaprajapati8119
    @nehaprajapati8119 3 роки тому +4

    SIR , FROM 00:00 TO 46:52 AGP &HP KI KATRE KATRE SAMAJ AGYI EK DAM BHANNNAT TRIKE SE❤️

    • @vinayakpawar505
      @vinayakpawar505 3 роки тому +1

      Katre katre😂😂

    • @adii18s
      @adii18s 3 роки тому

      Your how much syllabus completed of class 11 for jee??

    • @nehaprajapati8119
      @nehaprajapati8119 3 роки тому

      @Aditian only sequences nd series kiya hai abhi baad me soche ge 12th ka calculus pura nhi hua h abhi to basics ata h bs

    • @adii18s
      @adii18s 3 роки тому

      @@nehaprajapati8119 jee 2022 aspirant??

  • @bhawarlalbhawarlal8958
    @bhawarlalbhawarlal8958 3 роки тому +2

    answer of home work question is 2unitsquare

  • @sauryanshdubey1485
    @sauryanshdubey1485 3 роки тому +21

    Yes sir golden ratio pr lecture chahiye hme 😍

  • @ayankose6851
    @ayankose6851 Рік тому

    Sir
    Agar question aya cos(x-y), cosx, cos(x+y) -------hp me ahe
    So find cosx, 1/secx=______

  • @KrishnaGuptaTech
    @KrishnaGuptaTech 3 роки тому +5

    Sir Ji Syllabus Ke baad Golden Ratio pr vdo bnaadena🔥 thank u sir ji❤️

  • @shilpachoudhary6037
    @shilpachoudhary6037 3 роки тому +4

    Yes sir please make video on GOLDEN RATIO 🔥

  • @instrumentalrockers6864
    @instrumentalrockers6864 Рік тому +1

    sir got it the question at 24:22 as 9/2 sir
    LOVELY SESSION SIR ❣

  • @aadarshani493
    @aadarshani493 Рік тому +2

    U r best teacher of math sir 😍❤

  • @sayanbala6191
    @sayanbala6191 3 місяці тому

    Hw Answer
    2, 1, 1/2, 1/4, ....
    S = 4[1 - 1/2^(n-1)] unit^2 (simplified)
    if n = ∞
    S = 4 unit^2

  • @souvikghosh8632
    @souvikghosh8632 2 роки тому +4

    Very Helpful Sir...I have understood all concepts 🤗

  • @Sankdom_yt
    @Sankdom_yt 2 роки тому

    HW 4 is the sum it is an infinite decreasing gp with common ratio 1/2 and gp is 2,1,0.5,0.25------1/0

  • @authoryajat
    @authoryajat 3 роки тому +7

    41:30 yes sir please do that golden ratio lecture seems quite interesting

    • @darakhshayasmeen
      @darakhshayasmeen 3 роки тому +3

      Kaise itne aage pahunch gye🤔🤔🤔🤔

    • @bhannaataspirant2403
      @bhannaataspirant2403 3 роки тому +2

      @@darakhshayasmeen direct last 10 min se dekhke🤣🤣🤣

    • @iit1949
      @iit1949 3 роки тому

      are bhai 🙄kitne speed pe dekh rahe the 😂

    • @bhannaataspirant2403
      @bhannaataspirant2403 3 роки тому +1

      @@iit1949 time travel kiya he saayad🤣🤣

    • @iit1949
      @iit1949 3 роки тому

      @@bhannaataspirant2403 😂😂oo bhai 😂

  • @fahadshabbir4458
    @fahadshabbir4458 3 роки тому +1

    Answer of last homework question
    A1 + A2 + A3+...... is ( 4 )

  • @interestingphysics3562
    @interestingphysics3562 3 роки тому +10

    Thanks sir for providing a great lecture 👌 👍

    • @IshaansGoodLife
      @IshaansGoodLife 3 роки тому

      ua-cam.com/video/GvMtPtnQGdA/v-deo.html Alakh Sir on Hud Hud Dabangg 😂😂😂😂

    • @akshay_anand360
      @akshay_anand360 3 роки тому +3

      ❤❤

  • @aditiyakumar3292
    @aditiyakumar3292 3 роки тому +1

    Hw question ans. 4unit^2 done by sum of infinite G.P.

  • @dideal2239
    @dideal2239 3 роки тому +5

    Don ki Bhannat 🔥 entry..
    To kaise hai aaplog 😍

  • @pintusha518
    @pintusha518 10 місяців тому +1

    46:19
    Ans -4 unit square

  • @asheeshkumar791
    @asheeshkumar791 3 роки тому +7

    13:54
    n-1 terms samajh me a gyi

  • @ooprigyan
    @ooprigyan 2 роки тому +2

    Yes sir golden ratio par video banaiye

  • @sumit2162
    @sumit2162 3 роки тому +20

    30:57 smjh rhe ho 😂😂

  • @nishantlamba.4463
    @nishantlamba.4463 3 роки тому +1

    Homework Question ka answer h
    4 unit ²
    2+1+(1/2)+(1/4)+(1/8)...

  • @Lucifer-pj8vc
    @Lucifer-pj8vc 3 роки тому +4

    Sir ek request hai😥🙏🙏🙏🙏 aap pls apni tabiyat ka khayaal rakhiye sir
    Syllabus chahe thoda rah bhi jaaye to koi baat nhi🙂

  • @soumojitgon7833
    @soumojitgon7833 3 роки тому +1

    Golden ratio =1.618 .Source-Super 30

  • @hyperluzo
    @hyperluzo 3 роки тому +15

    We want a special lecture of golden ratio

  • @monuwarabegum6823
    @monuwarabegum6823 3 роки тому +2

    Yes sir we are very interested to know about GOLDEN RATION.....🙏

  • @santoshrout9437
    @santoshrout9437 2 роки тому +5

    Sir gold to cahiye

  • @UROOZFATIMA190
    @UROOZFATIMA190 Рік тому +2

    Sir your teaching is just amazing

  • @Amitkumar-ue6im
    @Amitkumar-ue6im 3 роки тому +2

    Answer of H.W question is 1 unit².

  • @pritamrajsatsangi4884
    @pritamrajsatsangi4884 3 роки тому +7

    Bhannatt shayari by aman sir
    To kaise hai aap log in style of carry

  • @goldenkinggaming211
    @goldenkinggaming211 3 роки тому +1

    Golden Ratio=1.6.8 ratio of every beautiful objects!! Am I right sir?

  • @unstablemultiverse1774
    @unstablemultiverse1774 3 роки тому +8

    "4" is the answer.

  • @kushalshedha4891
    @kushalshedha4891 Рік тому +2

    46:13 Sir Answer to homework ques is 4

  • @msanendh4861
    @msanendh4861 2 роки тому +3

    Sir we want a lecture on golden ratio

  • @yadunandanprasadsinha
    @yadunandanprasadsinha Рік тому +2

    Is that "|x|

  • @SangeetaYadav-cv9xb
    @SangeetaYadav-cv9xb 3 роки тому +5

    Sir i need your help, my 11 th exams are on 6 th march maths paper how can i prepare for that, bt acquiring that i have not learn anything till now please help

    • @arora_geetanshu.14
      @arora_geetanshu.14 3 роки тому +1

      Do nceret book of maths

    • @sunillodwal7658
      @sunillodwal7658 3 роки тому +1

      Many of ncrts problem are actually good go on

    • @Praveen10gautam
      @Praveen10gautam 3 роки тому

      Jitna ho gya h use NCERT se kr le bhai bas ab toh yahi ho skta hai

  • @sanjithmuralidharan6425
    @sanjithmuralidharan6425 Рік тому +1

    Hello, I just wanted to say that sir made a mistake at 34:32,
    HP = 1/[a+(n-1)d] and not 1/a + (n-1)d

  • @rashijain202
    @rashijain202 2 роки тому +5

    YES SIR WE WANT A LECTURE ON GOLDEN RATIO !!!😃

  • @divikshashukla1573
    @divikshashukla1573 3 роки тому +2

    Yes sir ....please make video on Golden ratio
    Super 30 movie jbb se dekha h tb se Golden ratio ke baare me janna chahtui hu

  • @ushabaghel684
    @ushabaghel684 3 роки тому +3

    Yes sir we want lecture on golden ratio. Plz sir ❤️❤️.
    I didn't able to understand maths earlier because my teacher didn't explain me in this better way. Whenever i ask him about my dobuts. then he simply ignores me. And sometimes removes me from class, and used to say that u can't do it. You have taken wrong subject. He is too rude, I was really disappointed 😔😔.
    But you changed my perception towards mathematics. now i am understanding in best way. I can't thank you in these small words. You deserve a lot than these some lines. ❤️❤️.

    • @abhirupkundu2778
      @abhirupkundu2778 Рік тому

      The way you speak english makes sense as to why he cast you out of his classes and ignored you

  • @YT-he2yf
    @YT-he2yf 3 роки тому

    last question 4 sq unit sir....i got answer
    2+1+1/2+ 1/4 ......infinity
    Sn= a/(1-r) = 2/(1-1/2) = 4

  • @fmsflash9924
    @fmsflash9924 2 роки тому +3

    Golden ratio

  • @knd7196
    @knd7196 3 роки тому +1

    13:53 Ha Sir samajh mein aa gaya ekdum bhannatly🔥🔥

  • @shilpachoudhary6037
    @shilpachoudhary6037 3 роки тому +4

    Bhaannaat ❤️

  • @taranghotra8
    @taranghotra8 3 роки тому +1

    Sir padhate aise hae jaise hamme kuch bhi ni ata par question aese puchte hae Jaese hame sab ata hae

  • @bishalpatel1684
    @bishalpatel1684 3 роки тому +4

    Yes sir we want a lecture on "Golden Ratio"

  • @parmesh6892
    @parmesh6892 2 роки тому +1

    Ans of last que (HW) is 1

  • @ram_krishna_atish
    @ram_krishna_atish 3 роки тому +3

    Yes sir, we need a video on golden ratio 👍

  • @wakeawake2950
    @wakeawake2950 3 роки тому

    Golden ratio is nothing but (1+√5)/2 it a roots of this quadratic :
    x^2 - x-1= 0

  • @PrateekTripathiB-ul6vq
    @PrateekTripathiB-ul6vq 6 місяців тому +4

    Apne ko gold nhi golden ratio chahiye 😅

  • @IntenseBattler
    @IntenseBattler Рік тому +2

    42:25 sir aapne at a time kaise multiply and divide kiya ? Konsa rule hame ye batata hai?

  • @darakhshayasmeen
    @darakhshayasmeen 3 роки тому +4

    23:41 my ans is 9/2

  • @meenamishra8433
    @meenamishra8433 3 місяці тому

    Sir,
    You're wizard of Mathematics...❤

  • @mohdalam2995
    @mohdalam2995 3 роки тому +14

    I am bio student like karne ke liye aa hu

  • @imandeep_maheria
    @imandeep_maheria 10 місяців тому

    46:18 H.W. 2/1-√2
    Or. -2(1+2√2)

  • @djgamer5067
    @djgamer5067 Рік тому +3

    😊😊ok😊😊

  • @pushkarkulkarni9922
    @pushkarkulkarni9922 3 місяці тому +1

    Mast sir thanks make one short concept and only question practice video

  • @MaheshKumar-wv3oz
    @MaheshKumar-wv3oz 3 роки тому +4

    Sir limits kab hoga

    • @IshaansGoodLife
      @IshaansGoodLife 3 роки тому

      ua-cam.com/video/GvMtPtnQGdA/v-deo.html Alakh Sir on Hud Hud Dabangg 😂😂😂😂

  • @gourav1325
    @gourav1325 Рік тому +1

    Congratulations 🎉🎉🎉🎉 10 million subscribers

  • @bhukyapramod1923
    @bhukyapramod1923 3 роки тому +3

    Superb lecture full clarity sir❤️❤️❤️

  • @madhubenpatel4838
    @madhubenpatel4838 Рік тому

    Answer of the H.W. question in 4
    The areas will be 2, 1, 1/2, 1/4,........∞
    which are in G.P.

  • @Surajit25
    @Surajit25 3 роки тому +4

    13:54 (n-1) terms samaj me a gaya

  • @riya2059
    @riya2059 11 місяців тому +1

    Yes sir please make a video on golden ratio I am also curious about the sum of hp terms

  • @aryan3121
    @aryan3121 3 роки тому +2

    WE NEED GOLDEN RATIO QUESTION