Which one of the following series converges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$
B) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n }$
C) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 099 } }$

D) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { - 4 } }$
E)None of these

Question

Which one of the following series converges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$ 
B) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n }$ 
C) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 099 } }$

D) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { - 4 } }$ 
E)None of these

Quizplus · Accepted Answer

The series in option A converges because it is a p-series with $p > 1$ (specifically, $p = 1.0001$), and p-series converge if $p > 1$.

Which One of the Following Series Converges? A) ∑n=1∞1n1.0001\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }∑n=1∞​n1.00011​

Which One of the Following Series Converges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$