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?

The [math]-series [math] converges because:

Find the interval of convergence of [math].

Use the Lagrange error bound to estimate the maximum error in approximating [math] with the degree 2 Maclaurin polynomial.

Which test is best to determine convergence of [math]?

The power series [math] converges for which values of [math]?

The Taylor polynomial of degree 3 centered at [math] for [math] is used to approximate [math]. By the Lagrange error bound, the error is at most

Which of the following series converges conditionally?

The Taylor series for [math] centered at [math] is [math]. What is the radius of convergence?

Which of the following series converges conditionally? (I) [math] (II) [math] (III) [math]

The third-degree Taylor polynomial for [math] about [math] is used to approximate [math]. Using the Lagrange error bound, what is the maximum error of this approximation?