Unformatted text preview: he integral test to show that the series
converges. Then give a bound for the error in using
the partial sum S10 as an estimate for the sum S of the series.
gives the nth term for each positive integer n.
It is also strictly positive.
And since its derivative,
, is negative for all positive x-values, then the conditions of the
integral test are met. So then, the series converges if, and only if, the improper integral
The indefinite integral is so the definite integral is and the improper integral is
This much shows that the series converges.
The error involved in using S10 to estimate S is bounded by the improper integral, as follows. 7. Use the limit comparison test to determine whether the series to determine whether the series
converges. Specify the series
that you are using in your test, and keep trying until you find a series
I will use
, which converges by the p-series test. For this test we consider the limit Since this limit is finite, and the second series converges, then so does the first series. 8. Use the ratio test on the positive series to determine whether it converges. For the ratio t...
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This document was uploaded on 03/18/2014 for the course MATH 237 at Frostburg.
- Fall '1