Use the integral test to determine whether the series converges.
-$$\sum _ { n = 1 } ^ { \infty } \frac { 7 } { n }$$
A) diverges
B) converges

Question

Quizplus · Accepted Answer

We will use the integral test to determine the convergence of the series $\sum_{n=1}^\infty \frac{7}{n}$. Let $f(x) = \frac{7}{x}$, which is a continuous, positive, and decreasing function on $[1,\infty)$. Then,
$$\int_1^\infty \frac{7}{x}dx = 7\ln x \bigg|_1^\infty = \lim_{x	o\infty} 7\ln x - 7\ln 1 = \infty$$
Since the improper integral diverges, the series $\sum_{n=1}^\infty \frac{7}{n}$ also diverges by the integral test. Therefore, the answer is A) diverges.

Use the Integral Test to Determine Whether the Series Converges ∑n=1∞7n\sum _ { n = 1 } ^ { \infty } \frac { 7 } { n }n=1∑∞​n7​

Use the Integral Test to Determine Whether the Series Converges $\sum _ { n = 1 } ^ { \infty } \frac { 7 } { n }$