_________________________________________________________________________________

Calculus II Quiz
#11 May
13, 2003

Name____________________ R. Hammack Score
______

_________________________________________________________________________________

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 .