Series (1+1/n)^n, test for divergence | Summary and Q&A

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May 20, 2017
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blackpenredpen
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Series (1+1/n)^n, test for divergence

TL;DR

The video discusses using the test for divergence on a series with an exponent of N, concluding that the series diverges.

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Questions & Answers

Q: Can we use the root test on a series with an exponent of N?

No, the root test is not applicable to a series with an exponent of N. The limit of the series does not allow us to draw any conclusions.

Q: What other test can we use for this series?

The test for divergence can be used on the series with an exponent of N. By taking the limit of the original series, we find that it approaches the value of 'e'.

Q: Why is it important to show that the limit is not equal to zero when using the test for divergence?

When using the test for divergence, it is crucial to demonstrate that the limit of the series is not equal to zero. This is because a zero limit would not allow us to draw any conclusions about the convergence or divergence of the series.

Q: What is the conclusion drawn from applying the test for divergence on this series?

The conclusion is that the series, with the sum from 1 to infinity of (1 + 1/n)^n, diverges. This is determined by showing that the limit of the series is not equal to zero.

Summary & Key Takeaways

  • The video explores the possibility of using the root test on a series with an exponent of N, but concludes that it is not applicable.

  • The test for divergence is then used on the series, and it is found that the limit of the series does not equal zero.

  • Based on the test for divergence, it is concluded that the series diverges.

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