Question Number 106515 by nimnim last updated on 05/Aug/20 $${Sum}\:{up}\:{the}\:{following}\:{to}\:{nth}\:{term}: \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{3}}+\frac{\mathrm{10}}{\mathrm{8}}+\frac{\mathrm{17}}{\mathrm{15}}+\frac{\mathrm{26}}{\mathrm{24}}+…….. \\ $$ Answered by Dwaipayan Shikari last updated on 05/Aug/20 $${S}=\mathrm{1}+\frac{\mathrm{2}}{\mathrm{3}}+\mathrm{1}+\frac{\mathrm{2}}{\mathrm{8}}+\mathrm{1}+\frac{\mathrm{2}}{\mathrm{15}}+\mathrm{1}+\frac{\mathrm{2}}{\mathrm{24}}+.. \\ $$$${S}=\left(\mathrm{1}+\mathrm{1}+\mathrm{1}+…{n}\right)+\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{15}}+…\right)…
Question Number 40961 by Tawa1 last updated on 30/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jul/18 Commented by Tawa1 last updated on 30/Jul/18 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\…
Question Number 171998 by Mikenice last updated on 23/Jun/22 $${if} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{81},\:{then}\:{find}\: \\ $$$$\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{5}{x}} \\ $$ Terms of Service Privacy Policy…
Question Number 106457 by Rio Michael last updated on 05/Aug/20 Answered by bshahid010 last updated on 05/Aug/20 $${According}\:{to}\:{question}\: \\ $$$${T}_{\mathrm{5}} =\mathrm{50}\:\&\:{T}_{\mathrm{7}} =\mathrm{25} \\ $$$${Consider}\:{an}\:{AP}\:{with}\:{ist}\:{term}\:{a}\:{and}\: \\…
Question Number 106335 by Rio Michael last updated on 04/Aug/20 Commented by Rio Michael last updated on 04/Aug/20 $$\:\mathrm{Question}\:\mathrm{5}\:\mathrm{and}\:\mathrm{6}\:\mathrm{please} \\ $$ Terms of Service Privacy…
Question Number 171837 by Mikenice last updated on 21/Jun/22 $${solve}: \\ $$$$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{2} \\ $$$${x}+{y}=\mathrm{5}{xy} \\ $$ Answered by Rasheed.Sindhi last updated on 21/Jun/22 $$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{2}\Rightarrow{y}=\frac{\mathrm{2}−\mathrm{2}{x}}{\mathrm{3}} \\…
Question Number 40664 by Tawa1 last updated on 25/Jul/18 $$\mathrm{Factorise}:\:\:\:\:\:\mathrm{x}^{\mathrm{19}} \:−\:\mathrm{x}^{\mathrm{17}} \:+\:\mathrm{x}^{\mathrm{10}} \:+\:\mathrm{x}^{\mathrm{8}} \:+\:\mathrm{1} \\ $$ Answered by ajfour last updated on 26/Jul/18 $$\:=\:\left({x}^{\mathrm{10}} −{x}^{\mathrm{9}}…
Question Number 105571 by bobhans last updated on 30/Jul/20 $$\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}\:=? \\ $$ Answered by bubugne last updated on 30/Jul/20 $$\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}\:=\:\frac{\mathrm{0}.\mathrm{5}}{{n}+\mathrm{1}}−\frac{\mathrm{1}}{{n}+\mathrm{2}}+\frac{\mathrm{0}.\mathrm{5}}{{n}+\mathrm{3}} \\ $$$${S}_{{n}} \:=\:\Sigma\:\frac{{n}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}\:…
Question Number 105526 by bramlex last updated on 29/Jul/20 $$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}}+…+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+…+\mathrm{29}} \\ $$ Answered by Dwaipayan Shikari last updated on 29/Jul/20 $$ \\ $$$$ \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}+….+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+..+\mathrm{29}}\right)−\mathrm{1}…
Question Number 170980 by anas_zaidan last updated on 05/Jun/22 Answered by aleks041103 last updated on 05/Jun/22 $$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{2}} {ydxdy}= \\ $$$$=\left(\underset{\mathrm{0}} {\overset{\mathrm{1}}…