91Ó°ÊÓ

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. $$\sum_{n=1}^{\infty} \frac{1}{n^{0.2}}$$

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 \(a_{4}\). \(a_{n}=\frac{1}{n !}\)

Use the Ratio Test to determine if each series converges absolutely or diverges. $$\sum_{n=1}^{\infty}(-1)^{n} \frac{n+2}{3^{n}}$$

Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. $$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{n^{3 / 2}}$$

Find a formula for the \(n\)th partial sum of each series and use it to find the series' sum if the series converges. $$\frac{9}{100}+\frac{9}{100^{2}}+\frac{9}{100^{3}}+\dots+\frac{9}{100^{n}}+\dots$$

Find the first four terms of the binomial series for the functions. $$(1+x)^{1 / 3}$$

Use the Comparison Test to determine if each series converges or diverges. $$\sum_{n=1}^{\infty} \frac{n-1}{n^{4}+2}$$

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

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 \(a_{4}\). \(a_{n}=\frac{(-1)^{n+1}}{2 n-1}\)

(a) find the series' radius and interval of convergence. For what values of \(x\) does the series converge (b) absolutely, (c) conditionally? $$\sum_{n=0}^{\infty}(-1)^{n}(4 x+1)^{n}$$