Question

Does anyone know how to find if the following series is abs. conv, conditionally, conv, or not at all:
Sum from 1 to inf of (cos (1/n)/ n^2)

Answer 1

\[0<\sum_{n=1}^{+\infty}\frac{\cos{(1/n)}}{n^2}<\sum_{n=1}^{+\infty}\frac{1}{n^2}\]\[0<\sum_{n=1}^{+\infty}\frac{\cos{(1/n)}}{n^2}<\frac{\pi^2}{6}\]