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

h:[0,1] -> R is continuous

Prove that t(x) = [tex]\sum[/tex][tex]^{infinity}_{n=0}[/tex] x^{n}h(x^{n}) is uniformly convergent on [0,s] where 0<s<1

2. Relevant equations

3. The attempt at a solution

I have the definition of h being continuous but after this I am pretty clueless about how to tackle this problem. I could use the Weierstrass M-test. I know the series x^{n}converges uniformly on this interval as x^{n}< s^{n}but I don't know how to use the fact that h is continuous to find a sequence of real numbers that x^{n}h(x^{n}) is always less than.

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# Homework Help: Another uniform convergence question

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