Sequences And Series

Step 1: Analyze Series

P%20%3D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bn%7D

This is the harmonic series. It is a known result that the harmonic series:

%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bn%7D

is divergent even though the terms go to 0. So

P

is divergent.

Step 2: Analyze Series

Q%20%3D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bn%5E2%7D

This is a

p

-series with

p%20%3D%202

. The rule is:

%5Csum%20%5Cfrac%7B1%7D%7Bn%5Ep%7D%20%5Ctext%7B%20converges%20if%20%7D%20p%20%3E%201

Since

p%20%3D%202%20%3E%201

Q

is convergent.

Chapter Questions
1 MCQs