# radius of the power series

Find the radius of convergence of ∑▒〖(a_n x^n)〗, given a_n=1when n is the square of a natural number and a_n otherwise. If a_n=1 when n=m! for n∈N and a_n=0 otherwise, find the radius of convergence of ∑▒〖(a_n x^n)〗.

Determine the radius of convergence of ∑▒〖(a_n x^n)〗, if 0<ρ≤|a_n |≤q for all n∈N.

© BrainMass Inc. brainmass.com October 10, 2019, 12:37 am ad1c9bdddfhttps://brainmass.com/math/real-analysis/radius-power-series-298876

#### Solution Preview

To find the radius of the power series , we use the following theorem.

Theorem: Let , then the radius of convergence is .

Problem #1

(a) Find the radius of convergence of , given if is ...

#### Solution Summary

This job determines the radius of the power series.

$2.19