# series of (n^2+1)/(n^3+1), limit comparison vs direct comparison, calculus 2 tutorial | Summary and Q&A

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June 1, 2016
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blackpenredpen
series of (n^2+1)/(n^3+1), limit comparison vs direct comparison, calculus 2 tutorial

## TL;DR

The content discusses the divergence of the series Sigma 1/N^2 over N^3 using both the limit comparison test and the direct comparison test.

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### Q: What is the series being analyzed in the content?

The series being analyzed is Sigma 1/N^2 over N^3.

### Q: How is the divergence of the series determined using the limit comparison test?

The limit comparison test involves checking the limit as N goes to infinity and comparing the given series with a known divergent series, such as the harmonic series.

### Q: What is the result of applying the limit comparison test to the given series?

The limit comparison test shows that the given series is equivalent to the harmonic series, which is known to diverge.

### Q: How is the divergence of the series confirmed using the direct comparison test?

The direct comparison test involves comparing the given series with a known divergent series and showing that the given series is larger.

### Q: What is the conclusion of applying the direct comparison test to the given series?

The direct comparison test confirms that the given series is larger than the harmonic series, thereby proving its divergence.

## Summary & Key Takeaways

• The content explains the divergence of the series Sigma 1/N^2 over N^3 by simplifying the expression and reducing it to Sigma 1/N.

• The limit comparison test is used to compare the given series with the harmonic series, which is known to diverge.

• The direct comparison test is then used to show that the given series is larger than the harmonic series, confirming its divergence.