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Magazine Problem 259
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \cos ^{2} n$$
Problem 260
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \sin ^{2}(1 / n)$$
Problem 261
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \cos ^{2}(1 / n)$$
Problem 262
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \ln (1 / n)$$
Problem 263
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \ln \left(1+\frac{1}{n}\right)$$
Problem 264
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{n^{2}}{1+n^{4}}$$
Problem 265
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{n^{e}}{1+n^{\pi}}$$
Problem 266
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} 2^{1 / n}$$
Problem 267
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} n^{1 / n}$$
Problem 268
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n}\left(1-n^{1 / n}\right)$$
