Question

Consider the following series.
(a) Find the partial sums of s1, s2, s3, and s4. Use the pattern to guess a formula for S_n.
(b)Use mathematical induction to prove your guess.
(c) Show that the given infinite series is convergent and find its sum.

I have already done part (a) and have a guess for S_n.

Answer 1

is there any addition or attach file?

Answer 2

\[\sum_{n=1}^{\infty}{n\over {(n+1)!}}\]
\[S_n = {{{{(n+1)!}-1}}\over {(n+1)!}}\]