Exam 9: Infinte Series

Use a series to approximate to three decimal-place accuracy.

Find the interval of convergence for the series:

Determine whether or not the following series converges. If it converges, find its sum.

Determine whether or not the following series converges.

Use to determine if the sequence is strictly increasing, strictly decreasing, or neither.

Write out the first five terms of the sequence

Determine whether or not the following series converges. If it converges, find its sum.

Find the interval of convergence for the series:

Find the interval of convergence for the series:

Use differentiation to determine whether the sequence is strictly increasing or strictly decreasing, or neither.

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

Find the Maclaurin polynomial of order 3 for .

Determine whether or not the following series converges. Enter 'Yes' if the series converges, and 'No' if it diverges.

Determine whether or not the following series converges.

The following are the first five terms of an infinite sequence. Find a formula for the general term starting with n = 1 , and write down the entire sequence.

Find the third order Taylor polynomial for , centered at .

Find the first three nonzero terms of the Maclaurin series for the function by using an appropriate substitution in a known Maclaurin series and performing any algebraic operations that are required. State the radius of convergence of the series.

Find the Taylor polynomial of order 2 for , centered about .

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

How many terms of the following series are needed to insure that the difference between the resulting partial sum and the infinite series is < ?