Exam 10: Sequences and Infinite Series

Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. - , -1 < t $\le$ 1

Use the Comparison Test to determine if the series converges or diverges. -

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

Write the first four elements of the sequence. -

Solve the problem. -A patient takes 100 mg of medication every 24 hours. 80% of the medication in the blood is eliminated every 24 hours. a. Let d_n equal the amount of medication (in mg) in the blood stream after n doses, where d₁ = 100. Find a recurrence relation for d_n . b. Show that (d_n) is monotonic and bounded, and therefore converges. c. Find the limit of the sequence. What is the physical meaning of this limit?

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

Find the sum of the series. -

Find the infinite sum accurate to three decimal places. -

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

Find a formula for the nth term of the sequence. -0, 2, 2, 2, 0, 2, 2, 2 (0, 2, 2, 2 repeated)

Use the ratio test to determine if the series converges or diverges. -

Determine convergence or divergence of the series. -

Find the limit of the sequence if it converges; otherwise indicate divergence. - = 1 + +

Provide an appropriate response. -Which of the following statements is false?

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

Determine convergence or divergence of the series. -

Assume that the sequence converges and find its limit. - = 4, =

Solve the problem. -A ball is dropped from a height of 18 m and always rebounds of the height of the previous drop. How far does it travel (up and down) before coming to rest?

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

Use the ratio test to determine if the series converges or diverges. -