Q:

Finding the value of $ \sum_{n=5}^{204} (n - 2) $

Is there a generalized formula for finding a sum such as this one? I'm going over an old quiz for a programming class but I'm not able to solve it:
$$ \sum_{n=5}^{204} (n - 2) $$
I know this is probably dead simple, but I'm seriously lacking on the math side of computer science. 

A:

Hint:
$$ \sum_{i=1}^{n}i = \frac{n(n+1)}{2}, \quad  \sum_{i=1}^{n}1 = n.$$

A:

$$\sum_{n=5-4}^{204-4}((n+4)-2)=\sum_{n=1}^{200}(n+2)=\frac{200.(200+1)}{2}+2.200=20500$$

A:

The other answers mention that you require the sum $\sum_{1}^{k} n=\frac{k(k+1)}{2}$. It is also useful to note that $$\sum_{n=5}^{204}(n-2)=\sum_{n=3}^{202}n$$
This is called shifting the index, and to convince yourself it works you can just write out the first few terms of each side.

