Calculate integer summation when lower bound is a variable

Question

How do you calculate the following sum?

\begin{equation*} \sum_{i=k}^n i \end{equation*}

Answer 1

$\sum_{i=k}^n i = \sum_{i=0}^n i - \sum_{i=0}^{k-1} i = \frac{1}{2} \left[ n(n+1) - (k-1)k \right]$

Answer 2

This is a special case for the formula for the sum of n terms in an arithmetic progression:

http://en.wikipedia.org/wiki/Arithmetic_progression

Answer 3

Okay. I was able to find it here, thanks.

http://en.wikipedia.org/wiki/Summation#Some_summations_of_polynomial_expressions