Use the \(p\)-series test to decide whether \(\sum_{n=1}^{\infty}\frac{1}{n^2}\) converges or diverges.

Use the \(p\)-series test to decide whether \(\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}\) converges or diverges.

Use the geometric series test to decide whether \(\sum_{n=0}^{\infty}\left(\frac{3}{4}\right)^n\) converges or diverges.

Use the nth-term test to decide whether \(\sum_{n=1}^{\infty}\frac{n}{n+1}\) converges or diverges.

Use comparison to decide whether \(\sum_{n=1}^{\infty}\frac{1}{n^2+1}\) converges or diverges.

Use comparison to decide whether \(\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^2+1}}\) converges or diverges.

Use the ratio test to decide whether \(\sum_{n=1}^{\infty}\frac{n!}{5^n}\) converges or diverges.

Use the ratio test to decide whether \(\sum_{n=0}^{\infty}\frac{3^n}{n!}\) converges or diverges.

Decide whether \(\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}\) converges absolutely, converges conditionally, or diverges.

Use the integral test to decide whether \(\sum_{n=2}^{\infty}\frac{1}{n\ln n}\) converges or diverges.