In this section, we see that we can sometimes decide whether a series converges or diverges by comparing it to an improper integral.

MATH 142 - The Integral Test. Joe Foster. Practice Problems. Use the integral test to determine whether the following series converge or diverge. 1. ∞. X n=1. 1.

In this section we'll study several convergence tests that apply to series with positive terms. THE INTEGRAL TEST. Sample Problem #1: USING THE INTEGRAL TEST.

10.4 Integral Test for Convergence. Calculus. If the Integral Test applies, use it to determine whether the series converges or diverges.

sum is used to estimate the sum. Example Use the integral test to determine whether the series is convergent or divergent: ∞. X.

Determine if the series below converge or diverge. In case of convergence, find the sum of the series if possible. Note: the Integral Test is not ...

1 np converges for p > 1, diverges for p ≤ 1. Example Determine if the following series converge or diverge: ∞. X n=1.

The document discusses various tests for determining whether a series of positive terms converges or diverges, including: 1) The Integral Test, which relates ...

Integral Test. Let ​a​n​= ​f(n)​, where ​f(x)​is positive, decreasing, and continuous for . x ≥ 1. The integral test is valid if, ​f(x)​is positive, ...

The integral test and estimates of sums. Example 5. Determine if the series P. ∞ n=1 n2e−n3 converges or diverges. Solution: Use the integral test. Use f (x) ...