The following 2 tests prove convergence, but also prove the stronger fact that ∑ n a converges (absolute convergence). Ratio Test. If. 1 lim. 1 <. +. ∞. →.

Alternating Series Helps: 1) Before testing, pull out all of the (−1)n terms so that all the remaining terms are positive. 2) This test is only concerned ...

If an infinite geometric series Σarn is convergent, then its sum is a/(1− r) = a [1/(1- r)] p – Series: Σan = Σ (1/n)p is convergent for p>1 and is divergent ...

Here we will state the big theorems/tests we have learned to check for convergence and divergence of series. We will try to provide examples using a variety ...

Converges (absolutely) if L < 1. Diverges if L > 1 or if L is infinite. Inconclusive if L = 1. Useful if an involves factorials or nth powers. Root*. X an with ...

For convergence, find a larger convergent series. For divergence, find a smaller divergent series. LIMIT. COMPARISON. TEST. X.

Below is a set of guidelines for choosing an appropriate test. Guidelines for Testing a Series for Convergence or Divergence. 1. Does the nth term approach 0?

converge absolutely, converge conditionally, or diverge? Answer: Notice that ... are not going to zero, so the Divergence Test says that the series diverges.

In this unit we shall discuss special tests for convergence of a positive term series. We shall avoid using the word positive as we are considering only ...

4) Use the integral test to decide whether the following series converge or diverge. 1. ∞. X n=1. 1 n3. Answer: We use the integral test with f(x)=1/x3 to ...