Not a rigorous proof (I'll leave that to further investigation): S(n) = 1/n + 1/n^2 + ... = 1/n ( 1 + 1/n + 1/n^2 + ...) <--needs more justification in a rigo

Not a rigorous proof (I'll leave that to further investigation): S(n) = 1/n + 1/n^2 + ... = 1/n ( 1 + 1/n + 1/n^2 + ...) <--needs more justification in a rigorous proof S(n) = 1/n ( 1 + S(n) ) Simple algebra from here: n * S(n) - S(n) = 1 S(n) = 1 / (n-1)