converges or diverges ??

Question

Explain why the series below Explain why the series below converges or diverges using the p-series test. 

 

 

∑_(i=1)^∞  1/i^3

Answer 1

Hi Daniel.

 

The p-series test states

 

Σ(n=1-∞) 1/n^p

If p > 1 then the series converges

If 0 < p < 1 then the series diverges

 

Your series is

Σ(i=1-∞) 1/i³

 

Comparing the two series, p = 3

Since 3>1, then the series converges