Thread: Summation Induction help

Hello, I've read everything I can on induction for the most part it makes sense, but I'm having trouble with this summation problem:

SUM from i = 1 to n: (-1)^(i+1)(i^2) = [ (-1)^(n+1) n(n+1) ] / 2

(I dont know latex...yet)

Basis step:
1 = 1 check

Inductive step:
plugging in n+1 and trying to solve I can't seem to get anywhere...
Please point me in the right direction


Thank-you for any help!!
jeremywho

Well, I'll assume you know how induction is done and how it works. It's just a matter (in this case) of calculation. In fact, suppose the equality holds for some , that is:



You wish to prove it also holds for , hence you want to prove that:



Simply observe that:



and recall that you are assuming the equality is true for (which means you know the corresponding expression for that sum on the right side).

Hope it helped

Thank-you so much for the reply!!

I understand we want to prove this:


I don't understand how we get:



in



Maybe its just simple algebra I'm missing?

Thank-you Again!!

You just pick the last term of



which is and write it independently. A straightforward, numerical example:



The sums don't have the same upper bound! One ends in and the other in .

I finally got it! I just wanted to thank-you again for your help!