Question Number 10855 by Joel576 last updated on 27/Feb/17 $$\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}\:+\:\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}\:+\:\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}\:+\:…\:+\:\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!}\:=\:? \\ $$ Answered by nume1114 last updated on 28/Feb/17 $$\:\:\:\:\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}+\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+…+\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!} \\ $$$$=\underset{{n}=\mathrm{1}} {\overset{\mathrm{2014}} {\sum}}\frac{{n}+\mathrm{2}}{{n}!+\left({n}+\mathrm{1}\right)!+\left({n}+\mathrm{2}\right)!} \\…
Question Number 141890 by bekzodjumayev last updated on 24/May/21 Commented by bekzodjumayev last updated on 24/May/21 $$\boldsymbol{{Please}}\:\boldsymbol{{help}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 141665 by bekzodjumayev last updated on 22/May/21 Commented by bekzodjumayev last updated on 22/May/21 $${Please}\:{Help} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 10583 by Saham last updated on 19/Feb/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{4}^{\mathrm{th}\:} \:\mathrm{and}\:\mathrm{6}^{\mathrm{th}\:} \mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{is}\:\mathrm{42}.\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{third}\:\mathrm{and}\:\mathrm{9th}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{proression}\:\mathrm{is}\:\mathrm{52}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{term}\:,\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{10}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{progression}. \\ $$ Commented by Saham last updated…
Question Number 141640 by Willson last updated on 21/May/21 Answered by qaz last updated on 22/May/21 $$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{k}} \left(\mathrm{8}{k}+{n}\right)} \\ $$$$=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{k}} }\int_{\mathrm{0}}…
Question Number 141612 by Raxreedoroid last updated on 21/May/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} {C}_{{k}−\mathrm{1}} ^{\:{n}−\mathrm{2}} }{\left({k}+\mathrm{1}\right)^{{x}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10536 by ajfour last updated on 16/Feb/17 $${how}\:{can}\:{one}\:{rougly}\:\:{judge}\:\frac{\mathrm{548}}{\mathrm{879}}\:? \\ $$ Answered by ajfour last updated on 16/Feb/17 Terms of Service Privacy Policy Contact:…
Question Number 10521 by ajfour last updated on 16/Feb/17 $${A}\:{number}\:\left(\alpha\beta..\lambda…\mu\mathrm{2}\right)×\mathrm{2}\:=\left(\mathrm{2}\alpha\beta..\lambda…\mu\right) \\ $$$${find}\:{the}\:{number}. \\ $$$$ \\ $$ Answered by mrW1 last updated on 17/Feb/17 $$\left({Part}\:{I}\right) \\…
Question Number 10487 by Saham last updated on 13/Feb/17 $$\mathrm{A}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\mathrm{T}_{\mathrm{1}} ,\mathrm{T}_{\mathrm{2}} ,\mathrm{T}_{\mathrm{3}} ,…….\:\mathrm{T}_{\mathrm{n}\:} \mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{1}} \:+\:\mathrm{n}^{\mathrm{2}} \:=\:\mathrm{nT}_{\mathrm{n}} \:+\:\mathrm{2}\:\mathrm{for}\:\mathrm{all}\:\mathrm{integers} \\ $$$$\mathrm{n}\geqslant\mathrm{1}.\:\mathrm{if}\:\mathrm{T}_{\mathrm{1}} \:=\:\mathrm{2}.\:\mathrm{find}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:\mathrm{T}_{\mathrm{2}} ,\:\mathrm{T}_{\mathrm{3}}…
Question Number 10488 by Saham last updated on 13/Feb/17 $$\mathrm{An}\:\mathrm{exponential}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{terms}\:\mathrm{and}\:\mathrm{a} \\ $$$$\mathrm{linear}\:\mathrm{sequence}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{first}\:\mathrm{term}.\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{o}\:\mathrm{their}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is}\:\mathrm{3},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{second}\:\mathrm{term} \\ $$$$\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{2}},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{third}\:\mathrm{term}\:\mathrm{is}\:\mathrm{6}.\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{fifth}\:\mathrm{term}. \\ $$ Answered by mrW1 last updated…