[math-fun] sums involving all integer powers

I think somebody was recently asking about something like this. Let S be the set of powers>1 of integers>1, S={4,8,9,16,25,27,32,36....} then SUM 1/(x-1) = 1 and SUM 1/(x+1) = pi^2 / 3 - 5/2 where the sums are over x in S.