Exam 11: Infinite Sequences and Series

Find the exact value of the limit of the sequence defined by .

If $600 is invested at interest, compounded annually, then after n years the investment is worth dollars. Find the size of investment after 7 years.

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

Find a power series representation for the function and determine the radius of convergence.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Find the value of the limit for the sequence.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

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

Determine whether the given series is convergent or divergent.

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

Determine whether the series is convergent or divergent.

Use the power series for to estimate correct to four decimal places.

Test the series for convergence or divergence.

Determine whether the series is convergent or divergent. If it is convergent, write its sum. Otherwise write divergent.

An annuity is a sequence of payments made at regular intervals. Suppose that a sum of $200 is deposited at the end of each month into an account earning interest at the rate of 12% per year compounded monthly. Then the amount on deposit at the end of the month is . Consider the sequence defined by (a) Find the term of the sequence, and interpret your result. (b) Evaluate and interpret your result.

Determine which one of the p-series below is divergent.

Find the partial sum of the series . Give your answer to five decimal places.

Determine whether the given series is convergent or divergent.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

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