Question Number 32333 by abdo imad last updated on 23/Mar/18 $${decompose}\:{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)}\:{inside}\:{R}\left({x}\right). \\ $$ Commented by abdo imad last updated on 01/Apr/18 $${F}\left({x}\right)=\:\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{x}\right)}\:=\:\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}}…
Question Number 32334 by abdo imad last updated on 23/Mar/18 $${p}\:{is}\:{apolynomial}\:{having}\:{n}\:{roots}\:\:\left({x}_{{i}} \right)\:{with}\:{x}_{{i}} \neq{xj}\:{for} \\ $$$${i}\neq{j}\:\:{calculate}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{\mathrm{1}−{x}_{{k}} }\:. \\ $$ Commented by abdo imad last…
Question Number 32332 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\sum_{{p}=\mathrm{1}} ^{{n}} \:\:\:\frac{{p}}{\mathrm{1}+{p}^{\mathrm{2}} \:+{p}^{\mathrm{4}} }\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32331 by abdo imad last updated on 23/Mar/18 $${p}\:{is}\:{a}\:{polynomial}\:{having}\:{n}\:{simples}\:{roots}\:\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{i}\leqslant{n}} \\ $$$${prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{p}^{'} \left({x}_{{k}} \right)}\:=\mathrm{0} \\ $$ Terms of Service Privacy Policy…
Question Number 32330 by abdo imad last updated on 23/Mar/18 $${let}\:{p}_{{n}} \left({x}\right)=\left({x}+\mathrm{1}\right)^{\mathrm{6}{n}+\mathrm{1}} \:−{x}^{\mathrm{6}{n}+\mathrm{1}} \:−\mathrm{1}\:{with}\:{n}\:{integr} \\ $$$${prove}\:{that}\:\forall{n}\:\:\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} \:{divide}\:{p}_{{n}} \left({x}\right). \\ $$ Commented by abdo imad…
Question Number 32326 by abdo imad last updated on 23/Mar/18 $${simplify}\:\:\sum_{{k}={p}} ^{\mathrm{2}{p}} \:\:\:\:\:\frac{{C}_{{k}} ^{{p}} }{\mathrm{2}^{{k}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163396 by HongKing last updated on 06/Jan/22 $$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\mathrm{then}\:\:\Sigma\:\left(\mathrm{an}\:+\:\mathrm{b}\right)^{-\boldsymbol{\mathrm{p}}} \:\:\mathrm{converges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}>\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{diverges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}\leqslant\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163385 by HongKing last updated on 06/Jan/22 Answered by mahdipoor last updated on 06/Jan/22 $$\mathrm{5}+{e}^{{x}} {sin}\left({x}+\frac{\pi}{\mathrm{4}}\right)+{e}^{−{x}} {cos}\left({x}+\frac{\pi}{\mathrm{4}}\right)= \\ $$$$\mathrm{5}+\sqrt{\mathrm{2}}\left(\left(\frac{{e}^{{x}} +{e}^{−{x}} }{\mathrm{2}}\right){cosx}+\left(\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{2}}\right){sinx}\right)=…
Question Number 163383 by HongKing last updated on 06/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163378 by HongKing last updated on 06/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com