# radius of the power series

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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.

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#### 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.

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