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Category: Integration

let-I-n-0-1-2-1-2t-n-e-t-dt-with-n-integr-not-0-1-prove-that-t-0-1-2-1-e-1-2t-n-1-2t-n-e-t-1-2t-n-then-find-lim-n-I-n-2-prove-that-I-n-1-1-2-n-1-I-n

Question Number 30764 by abdo imad last updated on 25/Feb/18 letIn=012(12t)netdtwithnintegrnot01)provethatt[0,12]$$\frac{\mathrm{1}}{\:\sqrt{{e}}}\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \leqslant\:\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{e}^{−{t}} \:\leqslant\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{then}\:{find}\:{lim}_{{n}\rightarrow\infty\:} {I}_{{n}}…

dx-1-x-14-

Question Number 161830 by EnterUsername last updated on 22/Dec/21 dx1x14 Answered by Ar Brandon last updated on 22/Dec/21 $$\mathrm{arcsin}\left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)_{{n}}…