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Example 7: Text for Convergence

Test the series 09_infinite_series-226.gif for convergence.

If H is positive infinite then by Theorem 1 in Section 9.1,

ln H < Hc

09_infinite_series-227.gif for real c > 0.

Now take c so that 0 < c < 1. Then 2 - c > 1 so the p series 09_infinite_series-228.gif converges.

By the Limit Comparison Test, the given series 09_infinite_series-229.gif converges.

Last Update: 2006-11-15