## Friday, 23 July 2010

### A Strange Sequence Produces a Stranger Sum

Dave Richeson just posted a note from the annual meeting of The Euler Society.... One that caught my eye was

2. Let S={4,8,9,16,25,27,32,36,...) be the set of all nontrivial powers (listed without repeats). Christian Goldbach discovered the following really neat summation...

If you take each number in the set, reduce it by one, then take the reciprocal...they add up to one.... or

This is amazing to me because it is brilliant, beautiful, and yet, tells us (almost)nothing about the original set.

Euler proved this, Dave tells us, by starting with the infinite harmonic series... go figure...so what do you do in YOUR spare time.....