Determine whether the series 2n=1 2n+3 (1) converges absolutely, (2) converges conditionally, or (3) diverges

Determine whether the series 2n=1 2n+3 (1) converges absolutely, (2) converges conditionally, or (3) diverges. D (-1) 7. (4 points) Approximate the sum no with error less than 0.00001. Be sure to state how many terms in the sequence is the minimum number needed for this accuracy. Notice that n begins at zero! n! 8. (4 points) Find the interval of convergence for the power series no 100 (x+1)" ; be sure to also check the n33" endpoints of the interval for convergence if applicable. 5. Determine whether each of the following series converges or diverges. In each case be sure to (1) state the test you use, (2) run the test and (3) state your conclusion. a. (3 points) Σ 5(n+4) 2(n+3)(n+1) b. (3 points) 3+sinn 2n=1 72 +4n n4 C. (3 points) _ n=1 4" d. (3 points) {n-1 m2 +1 tan-In 4. Do each of the following series converge or diverge? Do not run a test; instead, describe in a complete sentence how you know upon visual inspection why each series converges or diverges. a. (2 points) ,57" b. (2 points) 2n=1 2n n=1 n15 D 3. For a series, -an, to converge to a sum, S, two sequences must converge. Fill in the blanks below. a. (1 point) lim an = n-00 b. (1 point) lim Sn 100 40 2. We are given the series 90 – 20+ 9 80 81 +... a. (2 points) Express this series using - notation. b. (2 points) Find the sum of this series if it converges; if it does not converge, then say so. D 1. The questions following have to do with the sequence { 3n+1 n+2 } 3n+1 and the series o n=1 n+2 a. (2 points) List the first three terms of the sequence. b. (2 points) Find the limit of the terms of the sequence. C. (2 points) List the first three terms of the sequence of partial sums of the series. d. 12 points) Determine if the series converges or diverges; be sure to state the test you use.