Determine if the following series converges or diverges and justify your decision.

The series converges by the root test since

Hence, the series converges.

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Stumbling Robot

A Fraction of a Dot
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Tag: Limits

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Test the given series for convergence or divergence

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Conclude if the given series converges or diverges and justify your conclusion

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Conclude if the given series converges or diverges and justify your conclusion

Determine if the following series converges or diverges and justify your decision.

The series converges by the root test since

Hence, the series converges.

Determine if the following series converges or diverges and justify your decision.

The series divergence by the comparison test. For we have

Thus,

which we know diverges. Hence, the given series diverges as well.

Determine if the following series converges or diverges and justify your decision.

The series diverges by the ratio test since

Hence, the series diverges.

Determine if the following series converges or diverges and justify your decision.

The series diverges by the ratio test since

Hence, the series diverges.

Determine if the following series converges or diverges and justify your decision.

This series diverges by the ratio test since

Hence, the series diverges.

Determine if the following series converges or diverges and justify your decision.

The series converges by the ratio test since

Hence, the series converges.

Determine if the following series converges or diverges and justify your decision.

The series converges by the ratio test since

Hence, the series converges.

Determine if the following series converges or diverges and justify your decision.

The series converges by the ratio test since

Hence, the series converges.

Test the following series for convergence or divergence. Justify the decision.

First, for , we have

(We know this since is decreasing on the interval , and so the area of the rectangle of width and height is greater than the area under the curve .) Then, this implies

But, we know converges; hence,

also converges.

Test the following series for convergence or divergence. Justify the decision.

The series converges since

We know the last series converges from a previous exercise (Section 10.14, Exercise #3).