Q. 3 - Calculus

Question

What is meant by a p-series?

Step-by-Step Solution

Answer

The series of the type $\sum _{k=1}^{\infty }\frac{1}{k^p}$ is called p-series.

Step 1. Given Information.

p-series.

Step 2. p- series.

The series of the type $\sum _{k=1}^{\infty }\frac{1}{k^p}$ are the p-series.

Step 3. Convergent of divergent.

The p-test states that:

(i) For $p>1$, the series $\sum _{k=1}^{\infty }\frac{1}{k^p}$ converges.

(ii) For $p=1$, the harmonic series $\sum _{k=1}^{\infty }\frac{1}{k}$ diverges.

(iii) For $p<1$, the series $\sum _{k=1}^{\infty }\frac{1}{k^p}$ diverges.