There is a simple solution of this problem for those who are not aware of mathematical induction. Let S1 = 1 + 2 + 3 + . . . +(n-2)+(n-1)+(n) We can also write by re-arranging S1 = (n) + (n-1) + (n-2)+ . . . + 3 + 2 + 1 Adding both equations 2S1 = (n+1) + (n+1) +( n+1) + . . . +(n+1) + (n+1) + (n+1) n terms 2S1 = n (n+1) Hence S1 = n (n+1)/2 Show less
This is not mathematical induction, this is the proof by series rather than the whole n=1, n=k, n=k+1 method or method of differences. I wouldn't recommend doing it this way, because its not on the mark scheme. Although it might be a creditable method I'd rather not take my chances on FP1.
It's better just to learn it the way he has shown it. There are alternative proofs to lots of things in mathematics; but, in general; it's worth knowing induction (broad technique) over those alternatives (usually less intuitive than induction). I've done enough tests involving proofs to know that induction is expected over and over, again.
Also, a lot of alternative proofs look like one-offs that suit for the particular scenario to be proven. Induction is broad and I've seen it used over and over in graph theory, alone. I used to dislike induction; but, it ends up feeling really easy, formulaic and intuitive.
Thankyou! The last bit helped things click for me, I'm using proof by induction whilst studying recursion. As it's true for the base case, and we've proved it's true for k+1, we know it's true for 2 and so on.
I watched your induction videos a number of months ago & I gotta say they're basically the best I've ever fucking seen on UA-cam. Helped me to like induction & see how easy it actually is. Sarada Herke does good proofs in graph theory, too. Other uploaders I've seen are just overrated & don't even cover different induction scenarios like these videos.
![Prove that 11^n - 4^n is divisible by 7 for any natural number, n. [Mathematical Induction]](http://i.ytimg.com/vi/pLbG3Vvpjjk/mqdefault.jpg)
There is a simple solution of this problem for those who are not aware of mathematical induction.
Let S1 = 1 + 2 + 3 + . . . +(n-2)+(n-1)+(n)
We can also write by re-arranging
S1 = (n) + (n-1) + (n-2)+ . . . + 3 + 2 + 1
Adding both equations
2S1 = (n+1) + (n+1) +( n+1) + . . . +(n+1) + (n+1) + (n+1) n terms
2S1 = n (n+1)
Hence S1 = n (n+1)/2
Show less
This is not mathematical induction, this is the proof by series rather than the whole n=1, n=k, n=k+1 method or method of differences. I wouldn't recommend doing it this way, because its not on the mark scheme. Although it might be a creditable method I'd rather not take my chances on FP1.
It's better just to learn it the way he has shown it. There are alternative proofs to lots of things in mathematics; but, in general; it's worth knowing induction (broad technique) over those alternatives (usually less intuitive than induction). I've done enough tests involving proofs to know that induction is expected over and over, again.
Also, a lot of alternative proofs look like one-offs that suit for the particular scenario to be proven. Induction is broad and I've seen it used over and over in graph theory, alone. I used to dislike induction; but, it ends up feeling really easy, formulaic and intuitive.
That was quick!
my exam is in an hour 30 and i just found this precious video which just saved my life
All the best for the exam !
Thankyou! The last bit helped things click for me, I'm using proof by induction whilst studying recursion. As it's true for the base case, and we've proved it's true for k+1, we know it's true for 2 and so on.
I watched your induction videos a number of months ago & I gotta say they're basically the best I've ever fucking seen on UA-cam. Helped me to like induction & see how easy it actually is. Sarada Herke does good proofs in graph theory, too. Other uploaders I've seen are just overrated & don't even cover different induction scenarios like these videos.
Good to hear
wonderful thank you!
i bet you won't get a better explanation than this....
Thank you. Gotta be flexible and embrace the dots.
Thanks
I love maths
I`m relly sorry but you have confused me even more
Oh dear!