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AlgebraQuestion and Answers: Page 268

Question Number 77883    Answers: 1   Comments: 7

Question Number 77881    Answers: 0   Comments: 5

Question Number 77864    Answers: 1   Comments: 1

Question Number 77855    Answers: 0   Comments: 0

Question Number 77819    Answers: 2   Comments: 0

Question Number 77804    Answers: 0   Comments: 2

Question Number 77800    Answers: 0   Comments: 0

if a_1 =1, a_2 =3 and a_n =(√(a_(n−1) +a_(n−2) )) with n≥3 find a_n in explicit form.

$${if}\:{a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}} =\sqrt{{a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} }\:{with}\:{n}\geqslant\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:{in}\:{explicit}\:{form}. \\ $$

Question Number 77799    Answers: 1   Comments: 0

if a_1 =3 and a_(n+1) =3a_n +6n^2 −12n+2 find a_n in terms of n.

$${if}\:{a}_{\mathrm{1}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +\mathrm{6}{n}^{\mathrm{2}} −\mathrm{12}{n}+\mathrm{2} \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$

Question Number 77741    Answers: 1   Comments: 1

Question Number 77725    Answers: 2   Comments: 4

Question Number 77721    Answers: 0   Comments: 1

Question Number 77604    Answers: 2   Comments: 0

given (((a−b)(b−c)(c−a))/((a+b)(b+c)(c+a)))=−(1/(30)) what the value of (b/(a+b))+(c/(b+c))+(a/(c+a)) ?

$${given} \\ $$$$\frac{\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right)}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}=−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${what}\:{the}\:{value}\:{of}\: \\ $$$$\frac{{b}}{{a}+{b}}+\frac{{c}}{{b}+{c}}+\frac{{a}}{{c}+{a}}\:? \\ $$

Question Number 77556    Answers: 0   Comments: 2

1. 1×1!×2!+2×2!×3!+3×3!×4!+....=? 2. ((1+(√2))/(2+(√3)))+((2+(√3))/(3+(√4)))+((3+(√4))/(4+(√5)))+......=? 3. (1/(1+(√2)+(√3)))+(2/((√2)+(√3)+(√4)))+(3/((√3)+(√4)+(√5)))+....=?

$$\mathrm{1}.\:\:\:\mathrm{1}×\mathrm{1}!×\mathrm{2}!+\mathrm{2}×\mathrm{2}!×\mathrm{3}!+\mathrm{3}×\mathrm{3}!×\mathrm{4}!+....=? \\ $$$$\mathrm{2}.\:\:\:\:\frac{\mathrm{1}+\sqrt{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\mathrm{3}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}+\sqrt{\mathrm{4}}}{\mathrm{4}+\sqrt{\mathrm{5}}}+......=? \\ $$$$\mathrm{3}.\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}}{\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{5}}}+....=?\: \\ $$

Question Number 77524    Answers: 1   Comments: 2

Question Number 77513    Answers: 0   Comments: 3

Question Number 77506    Answers: 1   Comments: 2

Question Number 77462    Answers: 0   Comments: 0

Question Number 77459    Answers: 1   Comments: 0

the greatest value of n so that only one value of k satisfies (8/(15))<(n/(n+k))<(7/(13)) is

$$ \\ $$$$ \\ $$$${the}\:{greatest}\:{value}\:{of}\:{n}\:{so}\:{that}\: \\ $$$${only}\:{one}\:{value}\:{of}\:{k}\:{satisfies}\: \\ $$$$\frac{\mathrm{8}}{\mathrm{15}}<\frac{{n}}{{n}+{k}}<\frac{\mathrm{7}}{\mathrm{13}}\:{is}\: \\ $$

Question Number 77451    Answers: 1   Comments: 1

Question Number 77412    Answers: 0   Comments: 7

Question Number 77379    Answers: 0   Comments: 0

Question Number 77377    Answers: 0   Comments: 0

Question Number 77346    Answers: 0   Comments: 3

Question Number 77340    Answers: 1   Comments: 0

Question Number 77313    Answers: 0   Comments: 4

x + y + z = 1 x^2 + y^2 + z^2 = 2 x^3 + y^3 + z^3 = 3 find x^8 + y^8 +z^8

$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{3} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{x}^{\mathrm{8}} \:+\:\mathrm{y}^{\mathrm{8}} \:+\mathrm{z}^{\mathrm{8}} \\ $$

Question Number 77219    Answers: 1   Comments: 0

if log_9 (a)=log_4 (a+b)=log_6 (b) what is (a/b) ?

$${if}\:\mathrm{log}_{\mathrm{9}} \left({a}\right)=\mathrm{log}_{\mathrm{4}} \left({a}+{b}\right)=\mathrm{log}_{\mathrm{6}} \left({b}\right)\: \\ $$$${what}\:{is}\:\frac{{a}}{{b}}\:? \\ $$

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