I got this question in homework:
Find an expression for the sum
$\sum k = 1 +\cdots + n$.
and prove it using an induction.
I'm not even near finding the expression. What I did notice is that if $n$ is (for example) 5 then the sum would be
$5^2 - 4^2 + 3^2 - 2^2 + 1^2$
So the first number is always positive and from there on the sign changes.
Any tips on how do I contintue from this point on, assuming I'm in the right direction?