Continuity and Differentiation

Let f(x) = sum(k=1..oo) (cos pi.x.9^k)/2^k, domain f = R.

For all x in R, the sequence denoted by f(x) converges.

If x in R,
is f continuous at x?
is f not differentiable at x?

I claim both are true.
To end this plight, a statement strong
Do prove me right or prove me wrong

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