# Series of n(1+n^2)^p, sect11.3#31 | Summary and Q&A

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May 14, 2017
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blackpenredpen
Series of n(1+n^2)^p, sect11.3#31

## TL;DR

The video explains how to determine the values of P for which a given series will converge using the integral test.

## Questions & Answers

### Q: What method does the video suggest for determining the convergence of the series?

The video recommends using the integral test to determine if the series converges.

### Q: How is the series converted into an improper integral?

By substituting U for the expression within the parentheses in the series, and replacing the DX term with DU/(2X), the series is transformed into an improper integral.

### Q: What is the condition for the series to converge according to the video?

The series will converge when P is less than 1.

### Q: Why is it necessary to convert the series into an improper integral?

By converting the series into an improper integral, the convergence of the series can be determined by analyzing the convergence of the integral.

## Summary & Key Takeaways

• The video demonstrates the use of the integral test to determine convergence of a series with a specific form.

• By converting the series to an improper integral and applying the integral test, the convergence of the series can be determined based on the value of P.

• The key conclusion is that the series will converge when P is less than 1.