91Ó°ÊÓ

Find an expression for the \(n\) th term of the sequence. (Assume that the pattern continues.) \(\left\\{\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \ldots\right\\}\)

Determine whether the geometric series converges or diverges. If it converges, find its sum. \(-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\cdots\)

Find an expression for the \(n\) th term of the sequence. (Assume that the pattern continues.) \(\left\\{\frac{3}{4}, \frac{4}{9}, \frac{5}{16}, \frac{6}{25}, \frac{7}{36}, \ldots\right\\}\)

Determine whether the series converges or diverges. $$ \sum_{n=2}^{\infty} \frac{(-1)^{n-1}}{\ln n} $$

Determine whether the series is convergent, absolutely convergent, conditionally convergent, or divergent. \(\sum_{n=1}^{\infty} \frac{(-1)^{n-1} n}{\sqrt{2 n^{2}+1}}\)

Find the radius of convergence and the interval of convergence of the power series. $$ \sum_{n=0}^{\infty} \frac{n ! x^{n}}{(2 n) !} $$

Use the Integral Test to determine whether the series is convergent or divergent. $$ \sum_{i=2}^{\infty} \frac{1}{n \sqrt{\ln n}} $$

Use the Comparison Test to determine whether the series is convergent or divergent. \(\sum_{n=3}^{\infty} \frac{3^{n}}{2^{n}-4}\)

Determine whether the series converges or diverges. $$ \sum_{n=2}^{\infty} \frac{(-1)^{n} n}{\ln n} $$

Use the Comparison Test to determine whether the series is convergent or divergent. \(\sum_{n=2}^{\infty} \frac{\ln n}{n}\)