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Category: Algebra

Sum-the-series-n-C-0-n-C-1-n-C-1-n-C-2-n-C-2-n-C-3-n-C-r-n-C-r-1-

Question Number 60416 by Tawa1 last updated on 20/May/19 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{0}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{3}} \:+\:…\:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}\:+\:\mathrm{1}}…

a-a-b-b-183-and-b-a-a-b-182-What-is-the-value-of-9-5-a-b-

Question Number 191486 by MATHEMATICSAM last updated on 24/Apr/23 $${a}\sqrt{{a}}\:+\:{b}\sqrt{{b}}\:=\:\mathrm{183}\:\mathrm{and}\:{b}\sqrt{{a}}\:+\:{a}\sqrt{{b}}\:=\:\mathrm{182} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{9}}{\mathrm{5}}\:\left({a}\:+\:{b}\right)\:? \\ $$ Answered by mr W last updated on 24/Apr/23 $${let}\:{A}=\sqrt{{a}} \\ $$$${B}=\sqrt{{b}}…

n-Z-Find-the-coefficient-of-x-1-in-the-expansion-of-1-x-n-1-1-x-n-

Question Number 60406 by Tawa1 last updated on 20/May/19 $$\mathrm{n}\:\in\:\mathbb{Z}^{+} ,\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:\mathrm{x}^{−\mathrm{1}} \:\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\:\:\left(\mathrm{1}\:+\:\mathrm{x}\right)^{\mathrm{n}} \left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{n}} \\ $$ Answered by mr W last updated on 20/May/19 $$\left(\mathrm{1}+{x}\right)^{{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{n}}…

Darren-McFaddden-of-Arkansas-placed-second-overall-in-the-Heisman-Trophy-voting-Players-are-given-3-points-for-every-first-place-vote-2-points-for-every-second-place-vote-and-1-point-for-every-thi

Question Number 125915 by john_santu last updated on 15/Dec/20 $${Darren}\:{McFaddden}\:{of}\:{Arkansas} \\ $$$${placed}\:{second}\:{overall}\:{in}\:{the}\:{Heisman} \\ $$$${Trophy}\:{voting}.\:{Players}\:{are}\:{given} \\ $$$$\mathrm{3}\:{points}\:{for}\:{every}\:{first}−{place}\:{vote}\: \\ $$$$,\:\mathrm{2}\:{points}\:{for}\:{every}\:{second}−{place}\:{vote} \\ $$$${and}\:\mathrm{1}\:{point}\:{for}\:{every}\:{third}−{place}\:{vote}. \\ $$$${McFadden}\:{received}\:\mathrm{490}\:{total}\:{votes} \\ $$$${for}\:{first}\:,\:{second}\:{and}\:{third}\:{place}\: \\…