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Question Number 45993 by peter frank last updated on 19/Oct/18 Commented by math khazana by abdo last updated on 20/Oct/18 $$\frac{{d}}{{dx}}\left({e}^{{x}^{\mathrm{2}} } \right)={lim}_{{h}\rightarrow\mathrm{0}} \:\frac{{e}^{\left({x}+{h}\right)^{\mathrm{2}} }…
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Question Number 111213 by mnjuly1970 last updated on 02/Sep/20 Answered by mathmax by abdo last updated on 02/Sep/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{2n}} \:\mathrm{cos}^{\mathrm{2}} \left(\frac{\mathrm{k}\pi}{\mathrm{2n}+\mathrm{1}}\right)\:\Rightarrow\mathrm{S}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{2}}\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{2n}}…
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