discrete mathematics - Finding a formula to sum natural numbers up to $n$

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?

Thanks!

Answer

Hint.

$$\begin{array}{cccccccccccc} & 1 & + & 2 & + & 3 & + & 4 & + & \cdots & + & n\\ +& n & + &n-1 & + & n-2 & + & n-3 & + & \cdots & + & 1\\ \hline & n+1 & + &n+1 & + &n+1 &+& n+1 & + & \cdots & + & n+1 \end{array}$$