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## Homework Statement

Show, from the definition of continuity, that the power series function f(x)=sum(a_n*x^n) is continuous for its radius of convergence.

## Homework Equations

Definition of continuity

## The Attempt at a Solution

Must show that for any |a| < R, given e>0 there exists d>0 such that |x-a|<d => |f(x) - f(a)|.

|f(x)-f(a)| < e.

|f(x) - f(a)| <= |f(x-a)|

Then I get stuck here.

Any help would be appreciated

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