91Ó°ÊÓ

Use a graphing utility to graph the first 10 terms of the sequence. $$ a_{n}=\frac{2}{3} n $$

Find the Maclaurin polynomial of degree \(n\) for the function. $$ f(x)=\frac{1}{x+1}, \quad n=4 $$

Use the Ratio Test to determine the convergence or divergence of the series. $$ \sum_{n=0}^{\infty} \frac{(-1)^{n} 2^{n}}{n !} $$

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) $$ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}(x-5)^{n}}{n 5^{n}} $$

Use the power series \(\frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^{n} x^{n}\) to determine a power series, centered at 0, for the function. Identify the interval of convergence. $$ f(x)=\ln (x+1)=\int \frac{1}{x+1} d x $$

Determine the convergence or divergence of the series.\(\sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{(2 n-1) \pi}{2}\)

Find the Maclaurin series for the function. \(g(x)=e^{-3 x}\)

Use the power series \(\frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^{n} x^{n}\) to determine a power series, centered at 0, for the function. Identify the interval of convergence. $$ f(x)=\ln \left(1-x^{2}\right)=\int \frac{1}{1+x} d x-\int \frac{1}{1-x} d x $$

Find the Maclaurin polynomial of degree \(n\) for the function. $$ f(x)=\frac{x}{x+1}, \quad n=4 $$

Use the Ratio Test to determine the convergence or divergence of the series. $$ \sum_{n=1}^{\infty} \frac{(-1)^{n-1}(3 / 2)^{n}}{n^{2}} $$