# Test for divergence for the series of (2^k*k!)/(k+2)!, calculus 2 tutorial | Summary and Q&A

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May 28, 2016
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blackpenredpen
Test for divergence for the series of (2^k*k!)/(k+2)!, calculus 2 tutorial

## TL;DR

The video explains and demonstrates the divergence test for a series involving factorials and exponents.

## Key Insights

• 😑 The video explains the process of simplifying factorial expressions and cancelling terms.
• 🍉 The divergence test helps determine if a series converges or diverges based on the behavior of its terms.
• 👌 The limit as K approaches infinity is a critical factor in applying the divergence test.
• ❓ The comparison between exponential and quadratic growth helps establish the divergence of the series.
• 🏆 The test for divergence provides a straightforward method for determining the convergence or divergence of a series.
• 👌 The speaker emphasizes the importance of understanding the behavior of terms as K approaches infinity.
• 🏆 The video offers an alternative approach to solving the series divergence using the divergence test.

## Transcript

converge or diverge Sigma when K goes from 1 to infinity 2 to a case power times K factorial over K + 2 in the parentheses factorial the usual way to go about this is that because we have the factorials and we also have the king the exponent we should do this which is the ratio test but I did that for you guys already please check out the video dow... Read More

### Q: What is the purpose of the video?

The video aims to explain and demonstrate the application of the divergence test for a specific series involving factorials and exponents.

### Q: How does the speaker simplify the factorial expressions?

The speaker simplifies the factorials by expanding them and canceling out terms to obtain a simplified expression for the series.

### Q: What is the significance of the limit as K approaches infinity?

The limit is crucial in determining whether the series converges or diverges. If the limit equals zero, the series may converge, but if the limit is nonzero, the series diverges.

### Q: How does the speaker establish that the original series diverges?

By showing that the limit of the expression does not equal zero, the speaker concludes that the original series diverges.

## Summary & Key Takeaways

• The video discusses the application of the divergence test for a series with factorials and exponents.

• The speaker demonstrates the process of simplifying the expression and determining the limit as K approaches infinity.

• By showing that the limit does not equal zero, the speaker concludes that the original series diverges.