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Author: Tinku Tara

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Question Number 68616 by Rio Michael last updated on 14/Sep/19 $${given}\:{that}\:{a},{b}\:{and}\:{c}\:{are}\:{positive}\:{numbers}\:{other}\:{than}\:\mathrm{1} \\ $$$$,\:{show}\:{that}\:\:{log}_{{b}} {a}\:×\:{log}_{{c}} {b}\:×\:{log}_{{a}} {c}\:=\:\mathrm{1} \\ $$$${hence},\:{evaluate}\:\:\:{log}_{\mathrm{10}} \mathrm{25}\:×\:{log}_{\mathrm{2}} \mathrm{10}\:×\:{log}_{\mathrm{5}} \mathrm{4} \\ $$ Answered by…

Read-the-following-S-i-1-n-i-S-n-1-n-1-2-n-1-2-3-S-n-1-1-n-2-n-2-3-S-n-1-S-S-n-1-n-How-can-this-possibly-be-correct-

Question Number 3077 by Filup last updated on 04/Dec/15 $$\mathrm{Read}\:\mathrm{the}\:\mathrm{following}: \\ $$$$ \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{n}^{{i}!} \\ $$$${S}={n}^{\mathrm{1}} +{n}^{\mathrm{1}×\mathrm{2}} +{n}^{\mathrm{1}×\mathrm{2}×\mathrm{3}} +… \\ $$$${S}={n}^{\mathrm{1}} \left(\mathrm{1}+{n}^{\mathrm{2}} +{n}^{\mathrm{2}×\mathrm{3}}…

Question-68611

Question Number 68611 by TawaTawa last updated on 14/Sep/19 Answered by mind is power last updated on 15/Sep/19 $$\frac{\mathrm{1}}{{r}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{4}\left({r}−\mathrm{2}\right)}−\frac{\mathrm{1}}{\mathrm{4}\left({r}+\mathrm{2}\right)} \\ $$$$\Rightarrow\sum_{{r}=\mathrm{3}} ^{\mathrm{100}} \frac{\mathrm{1}}{{r}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{4}}\Sigma\left(\frac{\mathrm{1}}{{r}−\mathrm{2}}−\frac{\mathrm{1}}{{r}+\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{99}}−\frac{\mathrm{1}}{\mathrm{100}}−\frac{\mathrm{1}}{\mathrm{101}}−\frac{\mathrm{1}}{\mathrm{102}}\right)…

Question-68609

Question Number 68609 by TawaTawa last updated on 14/Sep/19 Commented by TawaTawa last updated on 14/Sep/19 $$\mathrm{I}\:\mathrm{got}\:\mathrm{4m}/\mathrm{s}^{\mathrm{2}} \:\:\:\mathrm{in}\:\mathrm{number}\:\mathrm{14},\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{check} \\ $$ Answered by mr W last…