Use the Comparison Test to determine if the series converges or diverges.
-$$\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 2 n + 7 \sqrt { n } }$$
A) diverges
B) converges

Question

Quizplus · Accepted Answer

We can compare the given series to the harmonic series $\sum \frac{1}{n}$. Notice that $\frac{1}{n} \leq \frac{5}{2n+7\sqrt{n}}$ for all $n \geq 1$, since $2n+7\sqrt{n} \geq 2n > n$. Since the harmonic series diverges, the given series diverges by the Comparison Test.

Use the Comparison Test to Determine If the Series Converges ∑n=1∞52n+7n\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 2 n + 7 \sqrt { n } }n=1∑∞​2n+7n​5​

Use the Comparison Test to Determine If the Series Converges $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 2 n + 7 \sqrt { n } }$