Find the series’ radius and interval of convergence. For what values of x does the series converge?

$$\sum _ { n = 0 } ^ { \infty } x ^ { n }$$

Find the series’ radius and interval of convergence. For what values of x does the series converge?

$$\sum _ { n = 0 } ^ { \infty } \frac { 3 ^ { n } x ^ { n } } { n ! }$$

Find the series’ radius and interval of convergence. For what values of x does the series converge?

$$\sum _ { n = 2 } ^ { \infty } \frac { x ^ { n } } { n \ln n }$$

Find the series’ radius and interval of convergence. For what values of x does the series converge?

$$\sum _ { n = 0 } ^ { \infty } \frac { x ^ { n } } { \sqrt { n ^ { 2 } + 3 } }$$

Describe the radius of convergence of a power series. Describe the interval of convergence of a power series.

What is the radius of convergence of a power series? What is the interval of convergence of a power series?

Find the series’ radius and interval of convergence. For what values of x does the series converge?

$$\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { n + 1 } } { \sqrt { n } + 3 }$$

Describe the radius of convergence of a power series. Describe the interval of convergence of a power series.

Use the given transformation to evaluate the integral. double integral (x-3y)dA, where R is the triangular region with vertices (0, 0), (2, 1) and (1, 2); x=2u+v, y=u+2v

Find the series’ radius and interval of convergence.

$$\sum _ { n = 1 } ^ { \infty } \frac { x ^ { n } } { \sqrt { n } }$$

Find the radius of convergence and the interval of convergence of the power series.

$$\sum^{\infty}_{n=2}\frac{x^n}{n(\ln n)^2}$$

Find the radius of convergence and the interval of convergence of the power series.

$$\sum^{\infty}_{n=1}\frac{x^n}{n^2}$$

Show how to rearrange the terms of the series from the specified exercise to form a divergent series.

$$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{1+n}{n^2}$$

Find the radius of convergence and the interval of convergence of the power series.

$$\sum^{\infty}_{n=0}\frac{x^n}{n+1}$$