Exam 11: Infinite Sequences and Series

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

Evaluate the indefinite integral as an infinite series.

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

Determine whether the sequence defined as follows is convergent or divergent.

Find the sum of the series.

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

Test the series for convergence or divergence.

Find an expression for the term of the sequence. (Assume that the pattern continues.)

Find the interval of convergence of the series.

Given the series estimate the error in using the partial sum by comparison with the series .

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

Find the Maclaurin series for using the definition of a Maclaurin serires.

Determine whether the series converges or diverges.

Write the partial sum of the converging series which represent the decimal number .

Write the first five terms of the sequence whose term is given.

Let where f is a continuous, positive, and decreasing function on and suppose that is convergent. Defining where and we have that Find the maximum error if the sum of the series is approximated by

Determine whether the given series is convergent or divergent.

Determine whether the series converges or diverges.

Find the Maclaurin series for f (x) using the definition of the Maclaurin series.

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