Use the Comparison Test to determine if the following series converges

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Use the Comparison Test to determine if the following series converges or diverges. ∑n = 1∞17 n2+23 Choose the correct answer below. A. The series is divergent because 1 n2 < 17 n2+23 for all n and ∑n = 1∞1 n2 is divergent. B. The series is convergent because 17 n2+23 < 1 n2 for all n and ∑n = 1∞1 n2 is convergent. C. The series is divergent because 1 n < 17 n2+23 for all n and the harmonic series is divergent. D. The series is convergent because 17 n2+23 < 1 n3 for all n and ∑n = 1∞1 n3 is convergent.

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Use the Comparison Test to determine if the following series converges or diverges.

\sum_{n = 1}^{\infty} \frac{1}{7 n^{2} + 23}

Choose the correct answer below. A. The series is divergent because

\frac{1}{n^{2}} < \frac{1}{7 n^{2} + 23}

for all

n

and

\sum_{n = 1}^{\infty} \frac{1}{n^{2}}

is divergent. B. The series is convergent because

\frac{1}{7 n^{2} + 23} < \frac{1}{n^{2}}

for all

n

and

\sum_{n = 1}^{\infty} \frac{1}{n^{2}}

is convergent. C. The series is divergent because

\frac{1}{n} < \frac{1}{7 n^{2} + 23}

for all

n

and the harmonic series is divergent. D. The series is convergent because

\frac{1}{7 n^{2} + 23} < \frac{1}{n^{3}}

for all

n

and

\sum_{n = 1}^{\infty} \frac{1}{n^{3}}

is convergent.

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