Question

Use the Direct Comparison Test to determine whether the following series converges or diverges. ?_{n=1}^{?} frac{1}{4n^2 + 1} Choose the correct choice below. A. The series is convergent because 0 ? ?_{n=1}^{?} frac{1}{4n^2 + 1} < ?_{n=1}^{?} frac{1}{n^3} for all n and ?_{n=1}^{?} frac{1}{n^3} is convergent. B. The series is divergent because 0 ? ?_{n=1}^{?} frac{1}{n} < ?_{n=1}^{?} frac{1}{4n^2 + 1} for all n and the harmonic series is divergent. C. The series is convergent because 0 ? ?_{n=1}^{?} frac{1}{4n^2 + 1} < ?_{n=1}^{?} frac{1}{n^2} for all n and ?_{n=1}^{?} frac{1}{n^2} is convergent. D. The series is divergent because 0 ? ?_{n=1}^{?} frac{1}{n^2} < ?_{n=1}^{?} frac{1}{4n^2 + 1} for all n and ?_{n=1}^{?} frac{1}{n^2} is divergent.

          Use the Direct Comparison Test to determine whether the following series converges or diverges.
?_{n=1}^{?} frac{1}{4n^2 + 1}
Choose the correct choice below.
A. The series is convergent because 0 ? ?_{n=1}^{?} frac{1}{4n^2 + 1} < ?_{n=1}^{?} frac{1}{n^3} for all n and ?_{n=1}^{?} frac{1}{n^3} is convergent.
B. The series is divergent because 0 ? ?_{n=1}^{?} frac{1}{n} < ?_{n=1}^{?} frac{1}{4n^2 + 1} for all n and the harmonic series is divergent.
C. The series is convergent because 0 ? ?_{n=1}^{?} frac{1}{4n^2 + 1} < ?_{n=1}^{?} frac{1}{n^2} for all n and ?_{n=1}^{?} frac{1}{n^2} is convergent.
D. The series is divergent because 0 ? ?_{n=1}^{?} frac{1}{n^2} < ?_{n=1}^{?} frac{1}{4n^2 + 1} for all n and ?_{n=1}^{?} frac{1}{n^2} is divergent.

$Use the Direct Comparison Test to determine whether the following series converges or diverges. ?n=1^? frac14n^2 + 1 Choose the correct choice below. A. The series is convergent because 0 ? ?n=1^? frac14n^2 + 1 < ?n=1^? frac1n^3 for all n and ?n=1^? frac1n^3 is convergent. B. The series is divergent because 0 ? ?n=1^? frac1n < ?n=1^? frac14n^2 + 1 for all n and the harmonic series is divergent. C. The series is convergent because 0 ? ?n=1^? frac14n^2 + 1 < ?n=1^? frac1n^2 for all n and ?n=1^? frac1n^2 is convergent. D. The series is divergent because 0 ? ?n=1^? frac1n^2 < ?n=1^? frac14n^2 + 1 for all n and ?n=1^? frac1n^2 is divergent.$

Added by Joseph J.

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