91Ó°ÊÓ

Determine whether the series is convergent or divergent. If it is convergent, find its sum. $$\sum_{n=1}^{\infty}\left[(0.8)^{n-1}-(0.3)^{n}\right]$$

\(9-32\) n Determine whether the sequence converges or diverges. If it converges, find the limit. $$a_{n}=\cos (2 / n)$$

Find a power series representation for the function and determine the radius of convergence. $$ f(x)=\frac{x^{2}+x}{(1-x)^{3}} $$

\(9-32\) n Determine whether the sequence converges or diverges. If it converges, find the limit. $$\left\\{\frac{(2 n-1) !}{(2 n+1) !}\right\\}$$

\(19-40=\) Determine whether the series is absolutely convergent, conditionally convergent, or divergent. $$ \sum_{n=0}^{\infty} \frac{(-10)^{n}}{n !} $$

Find a power series representation for \(f,\) and graph \(f\) and several partial sums \(s_{a}(x)\) on the same screen. What happens as \(n\) increases? $$ f(x)=\frac{x}{x^{2}+16} $$

Determine whether the series is convergent or divergent. If it is convergent, find its sum. $$\sum_{n=1}^{\infty} \arctan n$$

Find the radius of convergence and interval of convergence of the series. $$\sum_{n=1}^{\infty} \frac{x^{n}}{1 \cdot 3 \cdot 5 \cdot \cdot \cdots \cdot(2 n-1)}$$

Find the radius of convergence and interval of convergence of the series. $$\sum_{n=1}^{\infty} \frac{n^{2} x^{n}}{2 \cdot 4 \cdot 6 \cdot \cdots \cdot(2 n)}$$

\(9-32\) n Determine whether the sequence converges or diverges. If it converges, find the limit. $$a_{n}=\frac{\tan ^{-1} n}{n}$$