MATH 401 INTRODUCTION TO ANALYSIS-I, SPRING TERM 2016, PROBLEMS 10 Return by Monday 28th March 1. Prove, using the denition of a limit, that lim n n2 n = 0. +1 2. Prove, using the denition of a limit, that n2 + 1 = 1. n n2 + 3 lim 3. Let c be a xed positive number and an = 1 where c > 0. 1 + nc Use the denition of a limit to prove that an converges. 4. Prove that the sequence n diverges