(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

0<p<1

Suppose [tex]\sum[/tex][tex]^{infinity}_{k=0}[/tex] p(p-1)...(p-k+1)(-1)^{k}/k(k-1)...1 is convergent.

Show that [tex]\sum[/tex][tex]^{infinity}_{k=0}[/tex] p(p-1)...(p-k+1)(x)^{k}/k(k-1)...1 is uniformly convergent on [-1,0]

2. Relevant equations

3. The attempt at a solution

I have shown that p(p-1)...(p-k+1)(-1)^{k}/k(k-1)...1 < 0 for k=1,2,3,...

[tex]\sum[/tex][tex]^{infinity}_{k=0}[/tex] p(p-1)...(p-k+1)(-1)^{k}/k(k-1)...1 = L (< 0) as it converges to a limit.

|(-1)^{k}r^{k}|[tex]\leq[/tex] r^{k}for r<1 and -1<x[tex]\leq[/tex]0

However, I do not know how to tackle the case when x=-1.

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# Homework Help: Weierstrass M-test

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