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Magazine Problem 269
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} n\left(1-\cos \left(\frac{1}{n}\right)\right) \quad$$
Problem 270
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1}(\sqrt{n+1}-\sqrt{n})$$
Problem 271
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1}\left(\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\right) \quad$$
Problem 272
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1}(\ln (n+1)-\ln n)$$
Problem 273
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1} n\left(\tan ^{-1}(n+1)-\tan ^{-1} n\right)$$
Problem 274
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1}\left((n+1)^{2}-n^{2}\right)$$
Problem 275
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty}(-1)^{n+1}\left(\frac{1}{n}-\frac{1}{n+1}\right)$$
Problem 276
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}$$
Problem 277
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n^{1 / n}}$$
Problem 278
State whether each of the following series converges absolutely, conditionally, or not at all. $$\sum_{n=1}^{\infty} \frac{1}{n} \sin \left(\frac{n \pi}{2}\right)$$
