# Calc6.2

From Example Problems

Discuss the convergence of .

Again, use the integral test. Notice that the integral test states the series starts at and this series starts at . This does not change the fact that the integral test works. One extra term, or a million for that matter, will not change the convergence or divergence of a series. The one thing you must test is to make sure the function is continuous on the entire interval. For example, is undefined when so starting such a series at 0 would not work.

This integral converges to a real number. Since this function is continuous, positive, and decreasing, by the integral test, our series also converges.