For each series below, determine whether the series converges or diverges with a proper test, and write a sentence explaining why you chose the test you used. 1) X[infinity] n=1 n − 1 n3 + 1 2) X[infinity] n=1 (−1)n ln(n) √ n 3) X[infinity] n=1 n 2 e −n 3 4) X[infinity] k=1 1 3 + cos(k) 5) X[infinity] n=1 n! e n2