- #1

bedi

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## Homework Statement

Suppose c_n is the digit in the nth place of the decimal expansion of 2^1/2. Prove that the radius of convergence of [itex]\sum{c_n x^n}[/itex] is equal to 1.

## Homework Equations

## The Attempt at a Solution

What I want to show is that limsup |c_n|^1/n = 1. Clearly for any c_n, (c_n)^1/n ≥ 1. So we have sup (c_n)^1/n ≥ 1 for any n. It is also easy to see that sup (c_n)^1/n ≤ n^1/n for n large enough, as c_n is at most 9. So by the Sandwich lemma limsup |c_n|^1/n = 1.

Correct?