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## Homework Statement

So I get to Abel's Theorem and I'm like, "What the fork? I think I've seen this before."

## Homework Equations

**THEOREM III.**

*Suppose that the series ∑a*

_{n}x^{n}has a positive or infinte radius of convergence R. Let 0 < r < R. Then the series converges uniformly on the closed interval -r ≤ x ≤ r.**THEOREM XI.**

*If ∑a*

golds for -R ≤ x ≤ 0 if the series converges at x = -R.

_{n}x^{n}converges at x = R, then it converges uniformly on the closed interval 0 ≤ x ≤ R. A like conclusiongolds for -R ≤ x ≤ 0 if the series converges at x = -R.

## The Attempt at a Solution

Theorem 11 seems to be restating theorem 3 in a different way.

Theorem 2 mentions the "radius of convergence R." Theorem 11 mentions an R at which the series converges, which means R is any number inside the radius of convergence. Thus we're talking about the interval of convergence in both theorems. Then, basically, they both state that a series converges uniformly in its interval of convergence.

[PLAIN]http://images2.memegenerator.net/ImageMacro/4879227/lolwut.jpg?imageSize=Large&generatorName=OWL [Broken]

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