Exam 10: Sequences and Infinite Series

Solve the problem. -Mari drops a ball from a height of 19 meters and notices that on each bounce the ball returns to about of its previous height. About how far will ball travel before it comes to rest?

Determine if the series converges absolutely, converges, or diverges. -

Determine if the series converges or diverges. If the series converges, find its sum. -

Determine if the series converges or diverges. If the series converges, find its sum. -

Determine if the series converges absolutely, converges, or diverges. -

Determine convergence or divergence of the series. -

Find the limit of the sequence or state that it diverges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. -3 - 21 + 147 - 1029 + ... + 3 . + ...

Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. - + + + ... + + ...

Determine if the series converges or diverges. If the series converges, find its sum. -

Determine if the series converges absolutely, converges, or diverges. -

Find the infinite sum accurate to three decimal places. -

Find the limit of the sequence or determine that the limit does not exist. - =

Use the integral test to determine whether the series converges. -

Find the sum of the series. -

Express the number as the ratio of two integers. -0.77777 . . .

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

Find the sum of the series. -

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 1, =