Question Number 41707 by Necxx last updated on 11/Aug/18 $${Here}'{s}\:{a}\:{question}\:{that}\:{has} \\ $$$${troubled}\:{me}\:{for}\:{months}\:{now}.{Please} \\ $$$${help} \\ $$$$ \\ $$$$\mathrm{5}^{\sqrt{{x}}} \:−\:\mathrm{5}^{{x}−\mathrm{7}} \:=\mathrm{100} \\ $$$$ \\ $$$${find}\:{the}\:{possible}\:{value}\left({s}\right)\:{of}\:{x}. \\…
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Question Number 107187 by Dwaipayan Shikari last updated on 09/Aug/20 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\sqrt{\mathrm{8}}=\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{3}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}+\frac{\mathrm{3}.\mathrm{5}.\mathrm{7}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}+…… \\ $$ Commented by john santu last updated on 09/Aug/20 $$\sqrt{\mathrm{8}}\:=\:\sqrt{\mathrm{9}−\mathrm{1}}\:=\:\left(\mathrm{9}−\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\…
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Question Number 107178 by 175mohamed last updated on 09/Aug/20 Commented by mr W last updated on 09/Aug/20 $$=\frac{\sqrt{\mathrm{3}}−\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}−\sqrt{\mathrm{3}}}{\mathrm{2}}+…+\frac{\sqrt{\mathrm{169}}−\sqrt{\mathrm{167}}}{\mathrm{2}} \\ $$$$=\frac{\sqrt{\mathrm{169}}−\mathrm{1}}{\mathrm{2}} \\ $$$$=\mathrm{6} \\ $$ Answered…
Question Number 41642 by Tawa1 last updated on 10/Aug/18 $$\mathrm{n}\left(\mathrm{n}\:−\:\mathrm{1}\right)\left(\mathrm{n}\:−\:\mathrm{2}\right)\left(\mathrm{n}\:−\:\mathrm{3}\right)\:….\:\left(\mathrm{n}\:−\:\mathrm{r}\:+\:\mathrm{1}\right)\:=\:?? \\ $$ Answered by alex041103 last updated on 10/Aug/18 $$=\frac{{n}!}{\left({n}−{r}\right)!} \\ $$ Commented by Tawa1…
Question Number 172692 by mnjuly1970 last updated on 30/Jun/22 Answered by som(math1967) last updated on 30/Jun/22 Commented by som(math1967) last updated on 30/Jun/22 $${let}\:\angle{ABC}=\theta\:\:{side}\:{of}\:{square}={a} \\…
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Question Number 107101 by Dwaipayan Shikari last updated on 08/Aug/20 $$\mathrm{Fun}\:\mathrm{time} \\ $$$$ \\ $$$$\mathrm{1}+\mathrm{2x}+\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}^{\mathrm{3}} +….=\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} } \\ $$$$\mathrm{1}+\mathrm{4}+\mathrm{12}+\mathrm{32}+…=\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$\mathrm{4}+\mathrm{12}+\mathrm{32}+….=\mathrm{0}\:\:\left(\mathrm{No}\:\mathrm{1}\:\mathrm{fun}\right) \\ $$$$…
Question Number 107092 by 175mohamed last updated on 08/Aug/20 Commented by Dwaipayan Shikari last updated on 08/Aug/20 $$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by hgrocks last updated…