Unit 10: Infinite Sequences and Series

Which test shows that the series [math] converges?

Find the radius of convergence of [math].

The Maclaurin series for [math] is [math]. What is the Maclaurin series for [math]?

Find the sum of the geometric series [math].

Using the ratio test, determine the interval of convergence of [math].

The Taylor polynomial of degree 2 for [math] centered at [math] is:

If [math] is approximated by 3 terms, the alternating series error bound gives error at most:

Which of the following series converges? I. [math] II. [math] III. [math]

The radius of convergence of [math] is

The Taylor polynomial of degree 3 for [math] centered at [math] is

The Lagrange error bound for approximating [math] using the second-degree Maclaurin polynomial [math] is at most

Using the ratio test, the series [math] is

If [math], then [math]

The power series representation of [math] for [math] is

The interval of convergence of [math] is

The coefficient of [math] in the Maclaurin series for [math] is

Use the ratio test on [math].

Find the radius of convergence of [math].

Find the Taylor polynomial of degree 2 for [math] centered at [math].

Does [math] converge absolutely, conditionally, or diverge?