Cameron L.

asked • 03/10/21

Which one of the following series is convergent?

Which one of the following series is convergent?

A the summation from 1 to infinity of the quotient of 1 and the square root of the quantity n plus 1
B the summation from 1 to infinity of the quotient of 2 times n and the sum of 5 and n squared
C the summation from 1 to infinity of the quotient of n squared and e raised to the power of n cubed
D the summation from 1 to infinity of the quotient of 1 and the 4th root of n


1 Expert Answer

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Tom K. answered • 03/10/21

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A,D, and B for all n >= 3 is bounded below by 1/n, which is divergent, so they are divergent.

As e^(n^2) > n^4 for all n, n^2/e^(n^2) is bounded above by 1/n^2, which is converges, so this converges.

C Converges

(another way to show C is to show that the ratio goes to 0)

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