Re: Continuity

On 27 Apr 2005 17:09:20 -0700, "Tim" <rooroo.zhou@xxxxxxxxx> wrote:

>Let f(x) = \sum_{k=1}^n (Cos[9^n*Pi*x]/2^n)
>
>prove f(x) is continuous but not differentiable everywhere.

Oops. Didn't notice the typo until I saw William's reply.
What you wrote doesn't make much sense - as William points
out, your definition is just f(x) = n*Cos[9^n*Pi*x]/2^n,
which is surely not what you meant.

You meant to say that f(x) = \sum_{n=1}^infinity (Cos[9^n*Pi*x]/2^n).
To put that another way, f = lim f_n, where
f_n(x) = \sum_{k=1}^n (Cos[9^k*Pi*x]/2^k) .

************************

David C. Ullrich
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