A variation of Abel's summation formula is n=1Nf(n)g(n)=f(N)G(N)n=1N1(f(n+1)f(n))G(n),\sum_{n = 1}^N f(n)g(n) = f(N)G(N) - \sum_{n = 1}^{N - 1} (f(n + 1) - f(n))G(n), where G(n)=k=1ng(k).G(n) = \sum_{k = 1}^n g(k). Suppose that $\alpha \in ...