Question Number 30435 by abdo imad last updated on 22/Feb/18 $${let}\:\:{f}_{{n}} \left({x}\right)=\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{e}^{−{nx}} \:\:{calculate}\:\:\int_{\mathrm{1}} ^{{e}} \:{f}_{{n}} \left({x}\right){dx}. \\ $$ Terms of Service Privacy Policy…
Question Number 30434 by abdo imad last updated on 22/Feb/18 $${find}\:{the}\:{nature}\:{of}\:\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:{x}^{{n}!} \:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30433 by abdo imad last updated on 22/Feb/18 $${find}\:{the}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{n}^{\mathrm{2}{n}} }{\left({n}!\right)^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30431 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{x}^{{n}} }{\mathrm{1}−{x}^{{n}} }\:\:{with}\:{x}\in\left[\mathrm{0},\mathrm{1}\left[\:\:{prove}\:{that}\right.\right. \\ $$$${f}\left({x}\right)\sim_{{x}\rightarrow\mathrm{1}} \:\:\:\frac{{ln}\left(\mathrm{1}−{x}\right)}{{x}−\mathrm{1}}. \\ $$ Terms of Service Privacy Policy…
Question Number 161485 by bobhans last updated on 18/Dec/21 $$\:\mathrm{Find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\:\mathrm{y}=\frac{\mathrm{cos}\:\mathrm{4x}+\mathrm{4sin}\:\mathrm{4x}+\mathrm{1}}{\mathrm{cos}\:\mathrm{4x}+\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30415 by abdo imad last updated on 22/Feb/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}+\mathrm{1}}\:{C}_{{n}} ^{{k}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30414 by abdo imad last updated on 22/Feb/18 $${find}\:\:{the}\:{value}\:{of}\:\:\sum_{{p}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{p}\:\:} \:\frac{{C}_{{n}} ^{{p}} }{{p}+\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30412 by abdo imad last updated on 22/Feb/18 $$\left.{f}\left.\:{is}\:{a}\:{function}\:{increazing}\left({or}\:{decreazing}\right){on}\:\right]\mathrm{0},\mathrm{1}\right] \\ $$$${prove}\:{that}\:{lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{{n}}\sum_{{q}=\mathrm{1}} ^{{n}} {f}\left(\frac{{q}}{{n}}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}. \\ $$$$ \\ $$ Terms of Service…
Question Number 30407 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:{s}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} {nx}^{{n}} \:\:{and}\:{w}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{n}}{x}^{{n}−\mathrm{1}} \:\:{for}\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{s}\left({x}\right).{w}\left({x}\right)\:{at}\:{form}\:{of}\:{series} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{s}\left({x}\right).{w}\left({x}\right)\:{at}\:{form}\:{of}\:{function}. \\ $$ Terms of…
Question Number 95941 by mathmax by abdo last updated on 28/May/20 $$\mathrm{prove}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{sinx}}\:=\sum_{\mathrm{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{x}+\mathrm{n}\pi} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com