MATH-2212: Calculus of One Variable II Worksheet for sections 11.3, 11.4 Practice problems 1. Use the Integral Test to determine whether the given series converges or diverges. In(n) (a) n n=2 1 () n(ln n) n=2 (c) n en n=1 2. Use the Direct Comparison Test to determine whether the given series converges or diverges. (a) 2n 1 3n+1 n=1 21 (b) 3n - 1 n=1 n=1 (e) n=0 5 COS N (c) n 5 COS N (d) n5 (f) n=1 n=1 Cos n n +5 4 arctan(n n3.5 3. Use the Limit Comparison Test to determine whether the given series converges or diverges. (a) n - 4n+2 n - 4n+2 n5 3n+1 (c) n=2 n 5 - 3n+1 (e) () 5m - 4n+2 197n33n2+ 705 (d) 5n+ 3nn (f) 2n4 - 3 n=2 n=0 n=1 n=1 2n+1 3n - 1 5n+4n 3n+2n 4. Use any appropriate method or a combination of methods to determine whether the given series converges or diverges. (2) n3 (c) 3 sin 1 Cos (b) M n 1 n - 5 (d) 3 cos = (f) n n=2 n=1 n=2 n ln n n4 - 1 ((+) 2 3 - 2