Exam 11: Infinite Sequences and Series

Suppose that the radius of convergence of the power series is . What is the radius of convergence of the power series .

Use the binomial series to expand the function as a power series. Find the radius of convergence.

Determine whether the sequence converges or diverges. If it converges, find the limit.

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .

Express the number as a rational number.

Determine whether the series is convergent or divergent.

Which of the partial sums of the alternating series are overestimates of the total sum?

Use the Comparison Test to determine whether the series is convergent or divergent.

A rubber ball is dropped from a height of 5 m onto a flat surface. Each time the ball hits the surface, it rebounds to 50% of its previous height. Find the total distance the ball travels.

The terms of a series are defined recursively by the equations . Determine whether converges or diverges.

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

Determine whether the series is convergent or divergent.

Determine whether the series is convergent or divergent.

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

Determine whether the series converges or diverges.

Determine whether the given series is convergent or divergent.

Determine whether the series converges or diverges.

Determine whether the series converges or diverges.

Determine whether the given series converges or diverges. If it converges, find its sum.