Question Number 39520 by math khazana by abdo last updated on 07/Jul/18 $${if}\:\left(\mathrm{1}+{x}\right)^{{n}} \:=\sum_{{i}=\mathrm{0}} ^{{n}} \:{a}_{{i}} {x}^{{i}} \:\:\:\:{and} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}+\mathrm{1}} \:=\sum_{{i}=\mathrm{0}} ^{{n}+\mathrm{1}} \:{b}_{{i}} \:{x}^{{i}} \:\:{calculate}…
Question Number 39517 by math khazana by abdo last updated on 07/Jul/18 $${find}\:{radius}\:{of}\:\:{S}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} } \\ $$$${and}\:{calculate}\:{its}\:{sum} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:\:{and}\:\:\sum_{{n}=\mathrm{1}} ^{\infty}…
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Question Number 104919 by mathmax by abdo last updated on 24/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }} \\ $$$$\mathrm{finf}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right) \\ $$ Commented by malwaan last updated on 25/Jul/20…
Question Number 39380 by maxmathsup by imad last updated on 05/Jul/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 39376 by maxmathsup by imad last updated on 05/Jul/18 $${how}\:{to}\:{calculate}\:{the}\:{product}\:\left(\sum_{{n}=\mathrm{0}} ^{\infty} {a}_{{n}} {x}^{{n}} \right).\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:{b}_{{n}} \:{x}^{\mathrm{2}{n}} \right)? \\ $$ Terms of Service…
Question Number 39378 by maxmathsup by imad last updated on 05/Jul/18 $${study}\:{the}\:{derivability}\:{of} \\ $$$${f}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{nx}\:+\mathrm{1}} \\ $$ Commented by math khazana by abdo…
Question Number 104895 by mathmax by abdo last updated on 24/Jul/20 $$\left.\mathrm{1}\right)\:\mathrm{decompose}\:\mathrm{the}\:\mathrm{fraction}\:\:\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{sumA}\:=\:\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{4}} }\:\:\mathrm{and}\:\mathrm{B}\:=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty\:} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{4}} }…
Question Number 104891 by mathmax by abdo last updated on 24/Jul/20 $$\left.\mathrm{1}\right)\:\mathrm{decompose}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Answered by…
Question Number 39291 by math khazana by abdo last updated on 04/Jul/18 $${let}\:{f}\left({x}\right)=\frac{{e}^{−{x}^{\mathrm{2}} } }{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by abdo mathsup 649…