Question Number 8558 by Sopheak last updated on 16/Oct/16 Commented by FilupSmith last updated on 16/Oct/16 $${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}^{\mathrm{4}} }{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)} \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)}=\frac{{A}}{\mathrm{2}{k}−\mathrm{1}}+\frac{{B}}{\mathrm{2}{k}+\mathrm{1}} \\ $$$$\mathrm{1}={A}\left(\mathrm{2}{k}+\mathrm{1}\right)+{B}\left(\mathrm{2}{k}−\mathrm{1}\right)…
Question Number 8554 by Sopheak last updated on 16/Oct/16 $${Problem}\:.\mathrm{15} \\ $$$${Find}\:{the}\:{sum}\:{of} \\ $$$${S}=\:\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}+\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}+…+\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!} \\ $$$$\: \\ $$ Commented by Yozzias last updated on 16/Oct/16…
Question Number 8553 by Sopheak last updated on 16/Oct/16 Commented by Yozzias last updated on 16/Oct/16 $$\frac{\mathrm{1}}{\mathrm{n}!}−\frac{\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}=\frac{\mathrm{1}}{\mathrm{n}!}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{n}!}\left(\frac{\mathrm{n}+\mathrm{1}−\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right)=\frac{\mathrm{n}}{\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)}=\frac{\mathrm{n}}{\left(\mathrm{n}+\mathrm{1}\right)!} \\ $$ Answered by Yozzias last updated on…
Question Number 74087 by mr W last updated on 19/Nov/19 $$\left({Q}\mathrm{73828}\right) \\ $$$${prove}\:{that}\:{no}\:{cube}\:{exists}\:{whose}\:{corners} \\ $$$${are}\:{located}\:{on}\:{all}\:{faces}\:{of}\:{an}\:{other}\:{cube}. \\ $$ Commented by mr W last updated on 18/Nov/19…
Question Number 8550 by tawakalitu last updated on 15/Oct/16 Answered by ridwan balatif last updated on 16/Oct/16 Commented by tawakalitu last updated on 16/Oct/16 $$\mathrm{Wow}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.…
Question Number 139619 by I want to learn more last updated on 29/Apr/21 Answered by mr W last updated on 30/Apr/21 $${P}={pressure} \\ $$$${V}={volume}\:{of}\:{gas}\:\left({air}\right) \\…
Question Number 8545 by Rishabh#1 last updated on 15/Oct/16 $$\mathrm{18}:\mathrm{48}\:::\:\mathrm{180}:? \\ $$$$\mathrm{Answer}\:\mathrm{optioms} \\ $$$$\mathrm{a}.\:\mathrm{392}\:\mathrm{b}.\:\mathrm{294}\:\mathrm{c}.\mathrm{230} \\ $$ Commented by Rishabh#1 last updated on 16/Oct/16 $$\mathrm{Answer}\:\mathrm{given}\:\mathrm{is}\:\mathrm{294}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{not} \\…
Question Number 139618 by I want to learn more last updated on 29/Apr/21 Answered by mr W last updated on 29/Apr/21 $$\frac{\mathrm{0}.\mathrm{00015}×\mathrm{0}.\mathrm{4}×\mathrm{1000}}{\mathrm{0}.\mathrm{03}}=\mathrm{2}\:{mm} \\ $$$${a}\:{degree}\:{is}\:\mathrm{2}{mm}\:{length}\:{on}\:{the}\:{scale}. \\…
Question Number 139612 by 676597498 last updated on 29/Apr/21 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left(\sqrt{{x}}\right)}{{e}^{\mathrm{2}\pi\sqrt{{x}}} −\mathrm{1}}{dx}\:=\:\mathrm{1}−\frac{{e}}{\left({e}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 139609 by bemath last updated on 29/Apr/21 $$\mathrm{If}\:\mathrm{tan}\:\mathrm{14}°\:=\:\mathrm{x}\:\mathrm{then}\:\mathrm{tan}\:\mathrm{18}°\:=? \\ $$ Answered by qaz last updated on 29/Apr/21 $$\mathrm{18}°=\frac{\mathrm{18}×\mathrm{14}°}{\mathrm{14}}=\frac{\mathrm{9}}{\mathrm{7}}\mathrm{tan}^{−\mathrm{1}} {x} \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{18}°=\mathrm{tan}\:\left(\frac{\mathrm{9}}{\mathrm{7}}\mathrm{tan}^{−\mathrm{1}} {x}\right) \\…