Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How do you calculate the following sum?

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

share|cite|improve this question

3 Answers 3

up vote 3 down vote accepted

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

share|cite|improve this answer

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

share|cite|improve this answer
Thanks. I probably should have specified that I was looking for a direct formula or derivation. –  credford Aug 13 '10 at 22:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.