Math Olympiad | Find the sum of the series without using a Calculator | VIJAY Maths

[@Rocio62154]

SENSATIONAL!

[@hangthuy458]

3×27^5=3×3^3×5=3×3^15=3^16

[@mathpro926]

Nice solution ❤

[@ManojkantSamal]

^=read as to the power
*=read as square root
Let R=27
As per question
R^0+R^1+R^2+R^3+R^4+R^5=?
So, The given expression will be
1+R+R^2+R^3+R^4+R^5
=(1+R)+R^2(1+R)+R^4(1+R)
=(1+R)(1+R^2+R^4)
=(1+R){R^4+2R^2+1 -R^2}
=(1+R){(R^2+1)^2 -R^2}
=(1+27){(27^2+1)^2-27^2}
=28{(729+1)^2-729}
=28{730)^2-729}
=28{532900-729}
=(30-2)×(532171)
=(30×532171)-(2×532171)
=15965130-1064342
=14900788...(May be )

[@vijaymaths5483]

Not may be 😀 exactly right ✅️

[@walterwen2975]

Math Olympiad: 27⁵ + 27⁴ + 27³ + 27² + 27¹ + 27⁰ =?
27¹ + 27⁰ = 27 + 1 = 28
27² = (3³)² = 3⁶ = (3²)(3⁴) = (10 - 1)(81) = 810 - 81 = 729
27³ = 27(27²) = 3(10 - 1)(729) = 3(7290 - 729) = 3(6561) = 19683
27⁴ = 27(27³) = 3(10 - 1)(19683) = 3(196830 - 19683) = 3(177147) = 531441
27⁵ = 27(27⁴) = 3(10 - 1)(531441) = 3(5314410 - 531441) = 3(4782969) = 14348907
27⁵ + 27⁴ + 27³ + 27² + 27¹ + 27⁰ = 14348907 + 531441 + 19683 + 729 + 28 = 14900788

[@rohiniprasad622]

YOUR CALCULATION IS WRONG, THERE IS NO SUBSTRACTION..

[@skclctn2124]

बीच में साइन ठीक करें

[@changryu8128]

Sorry, typo. Let 27 = a. Let answer value = S. (a-1)S = a^6 -1. Therefore, S = (a^6 - 1) / (a - 1) = (27^6 - 1) / (27 - 1) = 14,900,788. So simple! Do not show the stupid method.

[@vijaymaths5483]

There are multiple methods for finding answers in mathematic subject and please keep in mind, there no one is is stupid method,it's depends on our thinking ability

[@adhavan2009]

Gp formula a(rpowern-1/r-1 =1(27power6-1/27-1