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Question Number 66183 by 0ister D1Id0 last updated on 10/Aug/19

$$\mathrm{why}\underset{j=1}{\sum ^{\mathrm{\infty }}}\frac{sin\left(j^{2}x\right)}{j^2}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{differantial}$$$$\mathrm{anywhere}??\mathrm{plz}\mathrm{ploof}....\mathrm{help}$$

Commented by mathmax by abdo last updated on 10/Aug/19

$$letS\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{sin\left(n^{2}x\right)}{n^2}thesumS\left(x\right)convergesunif.$$$$but\frac{dS}{dx}\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}cos\left(n^{2}x\right)dontconvergesunif.$$

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