Menu Close

Category: Arithmetic

n-1-n-n-1-n-2-n-3-

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)}\:…

1-1-2-1-1-2-3-1-1-2-3-4-1-1-2-3-4-29-

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-170980

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}}…

Question-170914

Question Number 170914 by mathlove last updated on 03/Jun/22 Commented by infinityaction last updated on 03/Jun/22 $${x}\:=\:\:\frac{\mathrm{1}}{\:^{\mathrm{3}} \sqrt{\mathrm{2}}\:−\mathrm{1}}\:\:\:\:\:\:\:{g}.{p}.\:{sum} \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{{x}}\:=\:^{\mathrm{3}} \sqrt{\mathrm{2}\:} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} \:=\:\mathrm{2} \\…

5-2-5-2-5-1-

Question Number 105018 by bemath last updated on 25/Jul/20 $$\frac{\sqrt{\sqrt{\mathrm{5}}+\mathrm{2}}\:+\:\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}}{\:\sqrt{\sqrt{\mathrm{5}}+\mathrm{1}}}\:? \\ $$ Commented by bemath last updated on 25/Jul/20 $${thank}\:{you}\:{all} \\ $$ Answered by som(math1967)…