Problem 1. Determine whether the following sequences are convergent or divergent. (a) 5n-+3 1 n2+n , n 21. (b) 307-n, n 21. (c) In(n + 1) - In(n), n 21. (d) nn, n 2 1. (Hint: consider the sequence bn = In(an). Note that if an converges if bn converges, and an diverges if bn diverges, so it's enough to study bn. ) (e) n2-n, n 2 1. (f) sin(" ) , n 2 1. (g) (1)" sin(n) n , n 2 1. (Hint: recall that | sin(n)|