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Calculus  II                                                        Quiz #11                                                  May 13, 2003

Name____________________                      R.  Hammack                                              Score ______
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Find the interval of convergence of the folloing power series.

(1)

Using the ratio test for absolute convergence:

Thus, for convergence, we must have , or   .

For x = 1/5, the series is  which is a convergent p-series. Thus the series converges for x = 1/5.

For x = -1/5, the series is  which is a convergent alternating series. Thus the series converges for x = -1/5.

Thus, the interval of convergence is .

(2)

Using the ratio test for absolute convergence:

Thus, for convergence, we must have , or   .

For x = 1, the series is  which is divergent by comparison with the divergent harmonic series ,   as .

For x = -1, the series is  which is a convergent alternating series. Thus the series converges for x = -1.

Thus, the interval of convergence is .