4. (P14, Page 34; i ) Prove that the sequence {sn} converges to 1 where {sn} is defined by 1 1 + 3- 2 1 for every index n. + (n + 1)(n) Sn = 2.1 1. 1 1 and then apply properties of convergent sequences. You can k +1* (Hint: first simplify sn by using (k + 1)k k 1 = 0 without proof.) use the fact that lim n+o n + 1

Vn² +1 - Prove that the sequence {an}n=1 ={ converges by following the following sequence of steps. n=1 Prove that {a,} is bounded. n=1