A sequence is defined by u(1)=0 and (1+n) * u(n+1) = n + u(n) for positive integer n. Prove that u(n) = 1 - 1/(n!).
Hence, find the exact value of the sum to infinity of (1 - u(r))/(2^r).
I can prove u(n) = 1 - 1/(n!) by mathematical induction.
May I know how to answer the "hence" part?