Is this functional series differentiable on (-1,1)? If it is could you give the full proof? $$\sum_{n=1}^{\infty}x^{n!}$$
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What are your thoughts? – lulu Oct 16 '17 at 19:00
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1Hint: a power series is differentiable on its open disk of convergence. – Julien Oct 16 '17 at 19:05
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When we throw members of power series away (like x^3,x^4,x^7... that cannot be in original series) we get original series. Also we know that power series is differentiable on (-1,1) and this series without some members is also differentiable on (-1,1). Am I right? – J.John Oct 16 '17 at 19:35