Question Number 22394 by Tinkutara last updated on 17/Oct/17 $$\mathrm{Prove}\:\mathrm{that}\::\:\frac{\:^{{n}} {C}_{\mathrm{0}} }{{n}}−\frac{\:^{{n}} {C}_{\mathrm{1}} }{{n}+\mathrm{1}}+\frac{\:^{{n}} {C}_{\mathrm{2}} }{{n}+\mathrm{2}}−…+\left(−\mathrm{1}\right)^{{n}} .\frac{\:^{{n}} {C}_{{n}} }{\mathrm{2}{n}}=\frac{\mathrm{1}}{{n}.^{\mathrm{2}{n}} {C}_{{n}} } \\ $$ Terms of…
Question Number 22392 by Tinkutara last updated on 17/Oct/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{coefficients} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{1025}} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{integer}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 87927 by john santu last updated on 07/Apr/20 $$\mathrm{x}+\sqrt{\mathrm{y}}\:=\:\mathrm{7} \\ $$$$\sqrt{\mathrm{x}}\:+\:\mathrm{y}\:=\:\mathrm{11} \\ $$$$\mathrm{find}\:\mathrm{x}+\mathrm{y}\: \\ $$ Commented by MJS last updated on 07/Apr/20 $$\mathrm{we}\:\mathrm{had}\:\mathrm{the}\:\mathrm{same}\:\mathrm{question}\:\mathrm{lately}…
Question Number 22389 by Tinkutara last updated on 17/Oct/17 $${Simplify}: \\ $$$$\:^{{n}−\mathrm{1}} {C}_{\mathrm{2}} +\mathrm{2}\:^{{n}−\mathrm{2}} {C}_{\mathrm{2}} +\mathrm{3}\:^{{n}−\mathrm{3}} {C}_{\mathrm{2}} +…+\left({n}−\mathrm{2}\right)\:^{\mathrm{2}} {C}_{\mathrm{2}} \\ $$ Terms of Service Privacy…
Question Number 22388 by gopikrishnan005@gmail.com last updated on 17/Oct/17 $${if}\:{t}_{\mathrm{1}} \:,{t}_{\mathrm{2}} \:{are}\:{the}\:{extremeties}\:{of}\:{any}\:{focal}\:{chord}\:{of}\:{the}\:{parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{ax},{then}\:{t}_{\mathrm{1}} {t}_{\mathrm{2}=} \\ $$ Answered by math solver last updated on 17/Oct/17 $$−\mathrm{1}.\:{do}\:{you}\:{want}\:{proof}\:?…
Question Number 153457 by 0731619 last updated on 07/Sep/21 Answered by liberty last updated on 07/Sep/21 $${x}=\mathrm{3}\Rightarrow{p}\left(\mathrm{3}\right)=\frac{{p}\left(\mathrm{4}\right)}{\mathrm{3}}=\frac{\mathrm{12}}{\mathrm{3}}=\mathrm{4} \\ $$$${x}=\mathrm{2}\Rightarrow{p}\left(\mathrm{2}\right)=\frac{{p}\left(\mathrm{3}\right)}{\mathrm{2}}=\frac{\mathrm{4}}{\mathrm{2}}=\mathrm{2} \\ $$ Answered by Rasheed.Sindhi last…
Question Number 22387 by gopikrishnan005@gmail.com last updated on 17/Oct/17 $${the}\:{arguments}\:{of}\:{n}^{{th}} \:{roots}\:{of}\:{a}\:{complex}\:{number}\:{differ}\:{by} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22386 by gopikrishnan005@gmail.com last updated on 17/Oct/17 $${equivalent}\:{matrices}\:{are}\:{obtained}\:{by} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 87920 by M±th+et£s last updated on 07/Apr/20 Commented by M±th+et£s last updated on 07/Apr/20 $${prove} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 153458 by liberty last updated on 07/Sep/21 $${Given}\:{a}\:{set}\:{consisting}\:{of}\:\mathrm{22}\:{integer} \\ $$$$\:{A}=\left\{\pm{a}_{\mathrm{1}} ,\pm{a}_{\mathrm{2}} ,…,\pm{a}_{\mathrm{11}} \right\}.\:{Show}\:{that} \\ $$$${exist}\:{subset}\:{of}\:{S}\:{with}\:{properties} \\ $$$$\left(\mathrm{1}\right)\:{for}\:{every}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{11}\: \\ $$$$\:{have}\:{least}\:{one}\:{between}\:{a}_{{i}} \:{or}\:−{a}_{{i}} \\ $$$$\:{element}\:{of}\:{S} \\…