Basic Analysis I — Real Analysis · Problem 2.5.1

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · series-partial-sums

Problem

Suppose the

k

th partial sum of

\sum_{n=1}^{\infty} x_n

s_k = \frac{k}{k+1}

. Find the series, that is, find

x_n

, prove that the series converges, and then find the limit.