(25 points) Determine if each series is convergent or divergent. Clearly state which test(s) you are using, verify that this(these) test(s) is(are) valid (if applicable), and give justification for...

(25 points) Determine if each series is convergent or divergent. Clearly state which test(s) you are using, verify that this(these) test(s) is(are) valid (if applicable), and give justification for your conclusion. (a) (4 points) X∞ n=2 n n+1 lnn n (b) (5 points) X∞ n=1 1 (n + 1) ln(n + 1) (c) (4 points) X∞ n=1 1 2n + √ n (d) (4 points) X∞ n=2 1 (nlnn) 2 (e) (4 points) X∞ n=0 (n!)3 (3n)! (f) (4 points) X∞ n=1 n n 3 1996+7n 4. (12 points) Find the radius and interval of convergence of the power series. Determine when the series is convergent absolutely or conditionally, and divergent. X∞ n=0 2 n · x n p (4n + 1) · 5 n