In the book: Test for convergence or divergence, using each test at least once. Identify which test was used. (a) nth-Term Test, (b) Geometric Series Test, (c) p-Series Test, (d) Telescoping Series Test, (e) Integral Test, (f) Direct Comparison Test, (g) Limit Comparison Test.
Problem number 30.
I tried to solve this problem with the Geometric Series Test which told me it converged to

, since |r| < 1, using

. This answer doesn't seem right. Could someone work out this problem? If I am correct, please work out the problem anyways, this will get stored since its an answer to a book problem this site supports. Thanks!