UseTheorem 9.11 to determine the convergence or divergence of the series. $$\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 0.86 } }$$
A) converges
B) diverges
C) Theorem $9.11$ inconclusive

Question

Quizplus · Accepted Answer

The p-series test states that if $\sum \frac{1}{n^p}$ is a series with $p>1$, then the series converges. In this case, $p=0.86<1$, and therefore the series diverges.

UseTheorem 9 ∑n=1∞1n0.86\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 0.86 } }n=1∑∞​n0.861​

UseTheorem 9 $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 0.86 } }$