I have a question about a particular formula that is supposed to be used to simplify difficult summations into telescoping series. The formula is as follows.
$\sum k(k+1) = \sum \frac{1}{3} \Big(k(k+1)(k+2) - (k-1)k(k+1)\Big) $ So now here is the question. How would this be used if one were to sum $k^3$? Thank you very much in advance and I sincerely apologize for any MathJax errors in advance.