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**Showcase_22** Oh WOW!

I wasn't expecting quite so much help. I was trying it myself and I was still getting a bit stuck on it (my typo when I wrote $\displaystyle (-1)^{n+1}$ was really throwing me).

Anyway, thanks a bundle. I'm going to attempt this question and solve it like there's no tomorrow!!!

After trying and SUCESSFULLY solved the problem: I used a method similar to Soroban's except I did it a little differently:

$\displaystyle (-1)^k \frac{(k+1)(k+2)}{2}+(-1)^k(k+1)^2-(-1)^k (k+1)^2 $

After a lot of working you end up with the required result.

I like your method bkarpuz. **Direct computation** is a method I haven't heard of before. It took me a few read-throughs but I finally got it. =D