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Determine whether 〉· is convergent. Specifically, use the Comparison Test to compare this series to a geometric series. Claim

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Answer #1

The given series is

on 7t 7t

To apply comparison test we can take the geometric series

2n 7l n-1 7tSo common ration is 3-4. This geometric series is convergent as the modulus of the common ratio is less than 1. Also note that

2m for all large n >1. So by comparison test the given series is convergent. The reason is the terms of the given series is less or equal to the terms of a convergent series. Note that comparison test can be applied to series of positive terms only.

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