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Question Number 80792 Answers: 1 Comments: 0

Π_(n=1) ^∞ [((2n)/(2n−1)).((2n)/(2n+1))] =?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left[\frac{\mathrm{2}{n}}{\mathrm{2}{n}−\mathrm{1}}.\frac{\mathrm{2}{n}}{\mathrm{2}{n}+\mathrm{1}}\right]\:=? \\ $$

Question Number 80788 Answers: 0 Comments: 0

Question Number 80786 Answers: 1 Comments: 5

Question Number 80780 Answers: 1 Comments: 1

2∙m^x + 3∙n^y = 18 min{ m^x ∙ n^y } = ?

$$\mathrm{2}\centerdot{m}^{{x}} \:+\:\mathrm{3}\centerdot{n}^{{y}} \:\:=\:\:\mathrm{18} \\ $$$${min}\left\{\:{m}^{{x}} \:\centerdot\:{n}^{{y}} \:\right\}\:=\:? \\ $$

Question Number 80777 Answers: 1 Comments: 0

If ^(n+2) C_8 :^(n−2) P_4 = 57 : 16, then the value of n is ......

$$\mathrm{If}\:\:^{{n}+\mathrm{2}} {C}_{\mathrm{8}} \::\:^{{n}−\mathrm{2}} {P}_{\mathrm{4}} =\:\mathrm{57}\::\:\mathrm{16},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{n}\:\mathrm{is}\:...... \\ $$

Question Number 80775 Answers: 0 Comments: 0

There are n straight lines in a plane, no two of which are parallel, and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

$$\mathrm{There}\:\mathrm{are}\:{n}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{in}\:\mathrm{a}\:\mathrm{plane}, \\ $$$$\mathrm{no}\:\mathrm{two}\:\mathrm{of}\:\mathrm{which}\:\mathrm{are}\:\mathrm{parallel},\:\mathrm{and}\:\mathrm{no} \\ $$$$\mathrm{three}\:\mathrm{pass}\:\mathrm{through}\:\mathrm{the}\:\mathrm{same}\:\mathrm{point}. \\ $$$$\mathrm{Their}\:\mathrm{points}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{are}\:\mathrm{joined}. \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{fresh}\:\mathrm{lines}\:\mathrm{thus}\: \\ $$$$\mathrm{obtained}\:\mathrm{is} \\ $$

Question Number 80770 Answers: 1 Comments: 1

∫x^2 +3x dx=..

$$\int\mathrm{x}^{\mathrm{2}} +\mathrm{3x}\:\mathrm{dx}=.. \\ $$

Question Number 80764 Answers: 1 Comments: 0

show that ∫_0 ^∞ x arctanh(e^(−αx) )dx=((7ζ(3))/(8α^2 ))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}\:{arctanh}\left({e}^{−\alpha{x}} \right){dx}=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)}{\mathrm{8}\alpha^{\mathrm{2}} } \\ $$

Question Number 80761 Answers: 0 Comments: 1

Question Number 80760 Answers: 0 Comments: 1

Question Number 80832 Answers: 1 Comments: 2

Identifier les chiffres de l′addition decimale que voici : UN+DOUX+DOUX+DOUX +DOUX=NEUF

$$\boldsymbol{{Identifier}}\:\boldsymbol{{les}}\:\boldsymbol{{chiffres}}\:\boldsymbol{{de}} \\ $$$$\boldsymbol{{l}}'\boldsymbol{{addition}}\:\boldsymbol{{decimale}}\:\boldsymbol{{que}} \\ $$$$\boldsymbol{{voici}}\:: \\ $$$$\boldsymbol{\mathrm{UN}}+\boldsymbol{\mathrm{DOUX}}+\boldsymbol{\mathrm{DOUX}}+\boldsymbol{\mathrm{DOUX}} \\ $$$$+\boldsymbol{\mathrm{DOUX}}=\boldsymbol{\mathrm{NEUF}} \\ $$

Question Number 80752 Answers: 1 Comments: 1

Question Number 80748 Answers: 1 Comments: 3

lim_(x→∞) (((x!)/x^x ))^(1/x) = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{x}!}{{x}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} \:=\:? \\ $$

Question Number 80747 Answers: 1 Comments: 1

Question Number 80746 Answers: 1 Comments: 2

what is constan term in expansion (1+3x)^5 ((3/x)+1)^2

$${what}\:{is}\:{constan}\:{term}\:{in}\:{expansion} \\ $$$$\left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{5}} \left(\frac{\mathrm{3}}{{x}}+\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 80739 Answers: 0 Comments: 2

cos^3 θ+2sin^2 θ=3 ^ θ∈(0,2π) what is θ ?

$$\mathrm{cos}\:^{\mathrm{3}} \theta+\mathrm{2sin}\:^{\mathrm{2}} \theta=\mathrm{3}\bar {\:}\theta\in\left(\mathrm{0},\mathrm{2}\pi\right) \\ $$$${what}\:{is}\:\theta\:? \\ $$

Question Number 80733 Answers: 0 Comments: 3

x^2 =2^x ⇒x=?

$$\mathrm{x}^{\mathrm{2}} =\mathrm{2}^{\mathrm{x}} \Rightarrow\mathrm{x}=? \\ $$

Question Number 80731 Answers: 1 Comments: 1

Question Number 80718 Answers: 0 Comments: 2

Evaluate: lim_(x→0) (x/(∣x∣))

$$\mathrm{Evaluate}:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{x}}{\mid\mathrm{x}\mid} \\ $$

Question Number 80708 Answers: 1 Comments: 3

find sum of the series Σ_(n=0) ^∞ (((−1)^n )/((2n+1)(2n+3)))

$${find}\:{sum}\:{of}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)} \\ $$

Question Number 80706 Answers: 1 Comments: 0

Question Number 80702 Answers: 1 Comments: 4

{ (((1/x)+(1/y)=34)),(((1/(√x))+(1/(√y))=23−(1/(√(xy))) )) :} find the solution.

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\mathrm{34}}\\{\frac{\mathrm{1}}{\sqrt{{x}}}+\frac{\mathrm{1}}{\sqrt{{y}}}=\mathrm{23}−\frac{\mathrm{1}}{\sqrt{{xy}}}\:}\end{cases} \\ $$$${find}\:{the}\:{solution}. \\ $$

Question Number 80690 Answers: 0 Comments: 2

Question Number 80689 Answers: 0 Comments: 1

Question Number 80688 Answers: 0 Comments: 1

Question Number 80687 Answers: 0 Comments: 2

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