Consider the series (a) Find the partial sums and s1, s2, s3. Do you recognize the denominators?

Question:

Consider the series

(a) Find the partial sums and s1, s2, s3. Do you recognize the denominators? Use the pattern to guess a formula for sn.
(b) Use mathematical induction to prove your guess.
(c) Show that the given infinite series is convergent, and find its sum.