# Series convergence & estimation

Contents

How can we tell whether a series converges or diverges? How can we find the value a series converges to? There is an impressive repository of tools that can help us with these questions. Learn all about it here.

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How can we tell whether a series converges or diverges? There is an impressive repository of tools that can help us with this question. In this tutorial, we will cover the basic tests: n-th term test, integral test, and p-series test. These tests can help us later on with the more elaborate convergence tests.

If the sum of a series must be smaller than the sum of another series that converges, then that series must converge as well. Makes sense, no? This notion, and similar ones, are at the basis of the comparison convergence tests.

The ratio test is one of the most useful tests for series convergence. Alternating series are a special class of series that have their own, very useful test for convergence.

We've spent a lot of time thinking about whether a series converges or diverges. But, even if we can determine that a series converges, how can we figure out what it converges to? This tutorial will show techniques of estimating what a series converges to, and for determining how good our estimates are. This is super useful because most series can't be precisely evaluated (like we were able to do with infinite geometric series).