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## Homework Statement

Suppose that [tex]\sum[/tex]a

_{n}x

^{n}has finite radius of convergence R and that a

_{n}>= 0 for all n. Show that if the series converges at R, then it also converges at -R.

## Homework Equations

## The Attempt at a Solution

Since the series converges at R, then I know that [tex]\sum[/tex]a

_{n}R

^{n}= M.

At -R, the series is the following: [tex]\sum[/tex]a

_{n}(-R)

^{n}= [tex]\sum[/tex](-1)

^{n}a

_{n}R

^{n}.

I'm not sure where to go from here. I thought I needed to use the alternating series test, but how can I know that a1 >= a2 >= ... >= an for all n? Do I know this because the series converges? Thanks for your help.