Question Number 3974 by Yozzii last updated on 26/Dec/15 $${Define}\:{the}\:{sequence}\:\left\{{a}_{{n}} \right\}\:{by}\:{the} \\ $$$${recursive}\:{formula}\: \\ $$$$\:\:\:{a}_{{n}+\mathrm{1}} ={ca}_{{n}} −{nr}^{{n}−\mathrm{1}} \:\:\:\left({n}\in\mathbb{Z},{n}\geqslant\mathrm{1}\right) \\ $$$${with}\:{a}_{\mathrm{1}} ={h}\:{and}\:{c},{r},{h}\in\mathbb{C},\:{c},{r}\neq\mathrm{0}. \\ $$$${Find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\…
Question Number 3927 by prakash jain last updated on 24/Dec/15 $$\mathrm{5}\:\mathrm{integers}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{randomly}\:\mathrm{from}\:\mathbb{Z}^{+} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{them}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5}. \\ $$ Commented by prakash jain last updated on 26/Dec/15…
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Question Number 134987 by 0731619177 last updated on 09/Mar/21 Answered by Olaf last updated on 09/Mar/21 $$\mathrm{I}_{\mathrm{2}} \left({k}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}\mathrm{sin}{x}\mathrm{cos}{x}}{\:\sqrt{\mathrm{1}−{k}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} {x}}}\:{dx} \\ $$$$\mathrm{I}_{\mathrm{2}} \left({k}\right)\:=\:−\frac{\mathrm{1}}{{k}^{\mathrm{2}}…
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Question Number 69436 by azizullah last updated on 23/Sep/19 Answered by $@ty@m123 last updated on 23/Sep/19 $$\left({x}+\mathrm{4}\right)=\mathrm{2}\left({x}−\mathrm{6}\right) \\ $$$${x}=\mathrm{16} \\ $$ Commented by azizullah last…
Question Number 134977 by 0731619177 last updated on 09/Mar/21 Answered by Ñï= last updated on 09/Mar/21 $${tanhx}=\frac{{x}}{\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{3}+\frac{{x}^{\mathrm{2}} }{\mathrm{5}+\frac{{x}^{\mathrm{2}} }{\mathrm{7}+…}}}} \\ $$$$\int_{{a}} ^{{b}} {tanhxdx}={ln}\left(\mathrm{cosh}\:{x}\right)\mid_{{a}} ^{{b}}…
Question Number 69431 by azizullah last updated on 23/Sep/19 Answered by Kunal12588 last updated on 23/Sep/19 $$\mathrm{120}={x}+{y}…\left(\mathrm{1}\right) \\ $$$${let}\:{x}>{y} \\ $$$$\mathrm{3}{y}=\mathrm{2}{x}…\left(\mathrm{2}\right) \\ $$$${from}\:\left(\mathrm{1}\right) \\ $$$$\mathrm{240}=\mathrm{2}{x}+\mathrm{2}{y}…
Question Number 69433 by azizullah last updated on 23/Sep/19 Answered by Kunal12588 last updated on 23/Sep/19 $$\mathrm{630}−\mathrm{7}{x}=\mathrm{3}{x} \\ $$$$\Rightarrow{x}=\mathrm{63} \\ $$ Commented by azizullah last…