Stuck on proof by induction

Hello,

I start to solve this, but got stacked. Have no idea how to move on :confused:

Anybody help me ? (Thinking)

Code:

`5+8+11+…+ (3n+2) = 1/2n(3n+7)`

n=1

5+8+11+…+ (3*1+2) = 1/2 *1 (3*1+7) => 5=5

n=k

5+8+11+…+ (3k+2) = 1/2 k(3k+7)

n=k+1

5+8+11+…+ (3(k+1)+2) = 1/2(k+1) (3(k+1)+7)

5+8+11+…+ (3k+5) = 1/2 (k+1) (3k+10)

5+8+11+…+ (3k+2) + (3k+5) = 1/2 (k+1) (3k+10)

1/2 k(3k+7) + (3k+5) = 1/2 (k+1) (3k+10)

1/2 [3k^2 + 10k + 5] = 1/2 (k+1) (3k+10)

=>

Re: Stuck on proof by induction

Hello everybody, again me :D

Now i'm trying to solve or prove this one:

1^2+2^2+3^2+....+n^2=n(n+1)(2n+1)/6

And I came to the third step where i got this one:

2k^3+10k^2+13k+6 on the LHS. I know that to solve this and get the same like on RHS, I need to work with division with polynoms, but even if i try to do that, still can't prove LHS=RHS.

Can anybody help me somehow? (Worried)

Thanks

Re: Stuck on proof by induction

I think it should be (2k^3+**9**k^2+13k+6) / 6.

Re: Stuck on proof by induction

One mistake and everything is screwed up :D But it's great when there is someone that can fix that :) Thanks a lot, I solve it

Re: Stuck on proof by induction

Re: Stuck on proof by induction