Posted by tpc at December 13th, 2008

I don’t believe I have seen the following identity before, although it is pretty easy to prove it by induction.
\displaystyle \sum_{i=1}^n i^5 + \sum_{i=1}^n i^7 = 2 ( \sum_{i=1}^n i)^4.
I should mention I saw it in Edward Barbeau’s book Power Play.