Help with summation I have been working on the following summation, which is a part of some bigger problem. 

$\sum_{i=1}^{n-2} \frac{i}{2(n-2)}$

Now I am stuck, because non of the formulas, that I know, seem to be suitable. 
I tried to solve it in so many ways, but I get a wrong answer-- compared to what the professor obtained. 

Hint:
If you know this formula:
$$\sum_{k=1}^ak=\frac{a(a+1)}2$$
Then you know this:
$$\sum_{i=1}^{n-2}\frac i{2(n-2)}=\frac1{2(n-2)}\sum_{i=1}^{n-2}i=\frac1{2(n-2)}\frac{(n-2)(n-1)}2=\frac{n-1}4$$
