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AlgebraQuestion and Answers: Page 265

Question Number 98844 Answers: 3 Comments: 0

Please explain: Σ_(1 ≤ i < j ≤ n) ij = Σ_(j = 2) ^n ((j(j − 1)j)/2) I want to know how L.H.S = R.H.S

Question Number 98842 Answers: 2 Comments: 1

let f(x) be a dolvnomial of degree 4 such that f(1)=1 , f(2)=2 ,f(3)=3,f(4)=4 then f(6)=?

$${let}\:{f}\left({x}\right)\:{be}\:{a}\:{dolvnomial}\:{of}\:{degree}\:\mathrm{4}\: \\ $$$${such}\:{that}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:,\:{f}\left(\mathrm{2}\right)=\mathrm{2}\:,{f}\left(\mathrm{3}\right)=\mathrm{3},{f}\left(\mathrm{4}\right)=\mathrm{4} \\ $$$${then}\:{f}\left(\mathrm{6}\right)=? \\ $$

Question Number 98818 Answers: 0 Comments: 0

Question Number 98770 Answers: 0 Comments: 2

Question Number 98761 Answers: 0 Comments: 5

(√(x+(√x) )) −(√(x−(√x))) = m(√(x/(x+(√x)))) m is a real parameter

$$\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}\:}\:−\sqrt{\mathrm{x}−\sqrt{\mathrm{x}}}\:=\:\mathrm{m}\sqrt{\frac{\mathrm{x}}{\mathrm{x}+\sqrt{\mathrm{x}}}} \\ $$$$\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{parameter} \\ $$

Question Number 98750 Answers: 0 Comments: 0

Question Number 98796 Answers: 2 Comments: 0

Question Number 98570 Answers: 1 Comments: 1

a,b,c>0 prove: (a/(√(a^2 +8bc)))+(b/(√(b^2 +8ac)))+(c/(√(c^2 +8ab)))≥1 help please...

$$\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}>\mathrm{0}\:\:\:\:\:\:\:\boldsymbol{{prove}}: \\ $$$$\frac{\boldsymbol{{a}}}{\sqrt{\boldsymbol{{a}}^{\mathrm{2}} +\mathrm{8}\boldsymbol{{bc}}}}+\frac{\boldsymbol{{b}}}{\sqrt{\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{8}\boldsymbol{{ac}}}}+\frac{\boldsymbol{{c}}}{\sqrt{\boldsymbol{{c}}^{\mathrm{2}} +\mathrm{8}\boldsymbol{{ab}}}}\geqslant\mathrm{1} \\ $$$$\boldsymbol{{help}}\:\boldsymbol{{please}}... \\ $$

Question Number 98521 Answers: 1 Comments: 0

Question Number 98613 Answers: 0 Comments: 0

Question Number 98448 Answers: 1 Comments: 5

6^(273) +8^(273) :49 prove the division

$$\:\:\:\:\:\:\:\mathrm{6}^{\mathrm{273}} +\mathrm{8}^{\mathrm{273}} \:\::\mathrm{49}\:\:\:\boldsymbol{{prove}}\:\:\boldsymbol{{the}}\:\:\boldsymbol{{divi}\mathrm{s}{ion}} \\ $$

Question Number 98416 Answers: 3 Comments: 0

Question Number 98280 Answers: 1 Comments: 0

Let {a_n } be a sequence such that a_1 = 2, a_(n + 1) = ((3a_n + 4)/(2a_n + 3)), n ≥ 1, find a_n

$$\boldsymbol{\mathrm{Let}}\:\:\left\{\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \right\}\:\:\boldsymbol{\mathrm{be}}\:\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sequence}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\:\:\boldsymbol{\mathrm{a}}_{\mathrm{1}} \:=\:\:\mathrm{2}, \\ $$$$\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:=\:\:\frac{\mathrm{3}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:+\:\:\mathrm{4}}{\mathrm{2}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:\:+\:\:\mathrm{3}},\:\:\:\:\:\boldsymbol{\mathrm{n}}\:\geqslant\:\mathrm{1},\:\:\:\:\:\boldsymbol{\mathrm{find}}\:\:\:\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \\ $$

Question Number 98268 Answers: 0 Comments: 7

let p(x) be a polynomial function of (n−1)^(th) degree and p(k)=k for k=1,2,3,...,n find p(0) and p(n+1). example: n=10

$${let}\:{p}\left({x}\right)\:{be}\:{a}\:{polynomial}\:{function}\:{of} \\ $$$$\left({n}−\mathrm{1}\right)^{{th}} \:{degree}\:{and} \\ $$$${p}\left({k}\right)={k}\:{for}\:{k}=\mathrm{1},\mathrm{2},\mathrm{3},...,{n} \\ $$$${find}\:{p}\left(\mathrm{0}\right)\:{and}\:{p}\left({n}+\mathrm{1}\right). \\ $$$${example}:\:{n}=\mathrm{10} \\ $$

Question Number 98267 Answers: 2 Comments: 0

∀ a,b>0 , a^2 +b^2 =1 prove that ((1/a)+(1/b))((b/(a^2 +1))+(a/(b^2 +1)))≥(8/3)

$$\forall\:{a},{b}>\mathrm{0}\:,\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\left(\frac{{b}}{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{a}}{{b}^{\mathrm{2}} +\mathrm{1}}\right)\geqslant\frac{\mathrm{8}}{\mathrm{3}} \\ $$

Question Number 98215 Answers: 3 Comments: 2

Find the nth term of the sequence {a_n } such that ((a_1 + a_2 + ... + a_n )/n) = n + (1/n) (n = 1, 2, 3, ...)

Question Number 98205 Answers: 1 Comments: 0

Find the nth term of the sequence {a_n } such that a_1 = 1, a_(n + 1) = (1/2)a_n + ((n^2 − 2n − 1)/(n^2 (n + 1)^2 )) (n = 1, 2, 3, ...)

Question Number 98192 Answers: 2 Comments: 1

Question Number 98293 Answers: 2 Comments: 0

Question Number 98130 Answers: 0 Comments: 0

Question Number 98077 Answers: 0 Comments: 4

Question Number 98073 Answers: 1 Comments: 2

solve (√(6−x)) = 6−x^2

$$\mathrm{solve}\:\sqrt{\mathrm{6}−\mathrm{x}}\:=\:\mathrm{6}−\mathrm{x}^{\mathrm{2}} \\ $$

Question Number 98067 Answers: 2 Comments: 0

Question Number 97968 Answers: 1 Comments: 1

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Question Number 99300 Answers: 1 Comments: 0

Find Σ_(n=1) ^∞ (1/((3n)!))=?

$$\mathrm{Find}\:\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{{n}}\right)!}=? \\ $$

Question Number 97936 Answers: 1 Comments: 1

Find the value of (√(45−(√(2000)) )) + (√(45+(√(2000))))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\sqrt{\mathrm{45}−\sqrt{\mathrm{2000}}\:}\:\:+\:\:\sqrt{\mathrm{45}+\sqrt{\mathrm{2000}}}\: \\ $$

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