91Ó°ÊÓ

Use the Comparison Test to determine if each series converges or diverges. $$\sum_{n=2}^{\infty} \frac{n+2}{n^{2}-n}$$

Find a formula for the \(n\)th partial sum of each series and use it to find the series' sum if the series converges. $$1-2+4-8+\cdots+(-1)^{n-1} 2^{n-1}+\cdots$$

(a) find the series' radius and interval of convergence. For what values of \(x\) does the series converge (b) absolutely, (c) conditionally? $$\sum_{n=1}^{\infty} \frac{(3 x-2)^{n}}{n}$$

Use the Integral Test to determine if the series converge or diverge. Be sure to check that the conditions of the Integral Test are satisfied. $$\sum_{n=1}^{\infty} \frac{1}{n+4}$$

Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. $$\sum_{n=2}^{\infty}(-1)^{n} \frac{4}{(\ln n)^{2}}$$

Find the first four terms of the binomial series for the functions. $$\left(1+\frac{x}{2}\right)^{-2}$$

Use the Integral Test to determine if the series converge or diverge. Be sure to check that the conditions of the Integral Test are satisfied. $$\sum_{n=1}^{\infty} e^{-2 n}$$

Use the Comparison Test to determine if each series converges or diverges. $$\sum_{n=1}^{\infty} \frac{\cos ^{2} n}{n^{3 / 2}}$$

Gives a formula for the \(n\) th term \(a_{n}\) of a sequence \(\left\\{a_{n}\right\\} .\) Find the values of \(a_{1}, a_{2}, a_{3},\) and \(a_{4}\). \(a_{n}=\frac{2^{n}}{2^{n+1}}\)

(a) find the series' radius and interval of convergence. For what values of \(x\) does the series converge (b) absolutely, (c) conditionally? $$\sum_{n=0}^{\infty} \frac{(x-2)^{n}}{10^{n}}$$