Example 7: Text for Convergence

Test the series for convergence.

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

ln H < H^c

for real c > 0.

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

By the Limit Comparison Test, the given series converges.