Determine the convergence or divergence of the series. $8 \cdot \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.15 } }$
A) converges
B) diverges
C) cannot be determined

Question

Quizplus · Accepted Answer

The series converges due to the p-test for series convergence, which states that a series of the form $\sum \frac{1}{n^p}$ converges if $p > 1$. Here, $p = 1.15 > 1$, so the series converges. The factor of 8 does not affect convergence.

Determine the Convergence or Divergence of the Series 8⋅∑n=1∞1n1.158 \cdot \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.15 } }8⋅∑n=1∞​n1.151​

Determine the Convergence or Divergence of the Series $8 \cdot \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.15 } }$