Please provide solutions for the following questions

Part IV: Sequences and Series 1. Determine the convergence or divergence of the sequence with the given nt"* term. If the sequence converges, find its limit. e\" 5n + 100 (@) an = a1 Answer: Converges to 0 (d) d, =In (GRJFW) Answer: Converges to _ n (b) b, =sin(nm) Answer: Convergesto 0 1 ( n o = 6 () i= BIE Answer: Sequence diverges 2. Evaluate the following sums: 100en TT (a) _ Answer: 100 2 ( b) E Answer: TT n=2 n2 + 2n n=1 3. Use an appropriate test to determine whether each of the following series converge absolutely, con- verge conditionally, or diverge: 1 n2on+1 (a) 10n - 3 Answer: Diverges (d) > Answer: Converges. n=1 n=1 n 7n (b ) E ( - 1 ) n Answer: Conditionally (e) 100 n2 +3 Answer: Converges. n! n=0 n=1 converges. Vn 1 (f ) (- 1) n Answer: Conditionally con- (c) n In(n) Answer: Diverges n +1 n=1 n=2 verges