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Question Number 154930 Answers: 0 Comments: 1

Question Number 154928 Answers: 0 Comments: 0

Prove:: Σ_(k=0) ^m ((m),(k) )^2 (((n+2m−k)),(( 2m)) )= (((m+n)),(( n)) )^2

$$\mathrm{Prove}::\:\:\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{m}} {\sum}}\begin{pmatrix}{\mathrm{m}}\\{\mathrm{k}}\end{pmatrix}^{\mathrm{2}} \begin{pmatrix}{\mathrm{n}+\mathrm{2m}−\mathrm{k}}\\{\:\:\:\:\:\:\mathrm{2m}}\end{pmatrix}=\begin{pmatrix}{\mathrm{m}+\mathrm{n}}\\{\:\:\:\:\mathrm{n}}\end{pmatrix}^{\mathrm{2}} \\ $$

Question Number 154907 Answers: 0 Comments: 2

∫_2 ^( 8) e^(2x) cos^2 x dx=?

$$\int_{\mathrm{2}} ^{\:\mathrm{8}} \:{e}^{\mathrm{2}{x}} \:\mathrm{cos}^{\mathrm{2}} {x}\:{dx}=? \\ $$

Question Number 154902 Answers: 0 Comments: 1

∫_0 ^(3/2) E(x^2 )dx

$$\int_{\mathrm{0}} ^{\frac{\mathrm{3}}{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 154896 Answers: 0 Comments: 2

find the following ?please S=Σ_(k=1) ^n (1/(k(k+1)(k+2)))

$${find}\:{the}\:{following}\:?{please} \\ $$$${S}=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)} \\ $$

Question Number 154893 Answers: 0 Comments: 0

Question Number 154892 Answers: 1 Comments: 2

Find: cos(((3π)/7)) + cos(((3π)/7)) (√(2 - 2cos(((3π)/7)))) = ?

$$\mathrm{Find}: \\ $$$$\mathrm{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:+\:\mathrm{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:\sqrt{\mathrm{2}\:-\:\mathrm{2cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}\:=\:? \\ $$

Question Number 154889 Answers: 0 Comments: 0

Question Number 154888 Answers: 1 Comments: 0

Question Number 154926 Answers: 1 Comments: 0

∫_0 ^1 ((2x^2 )/((x^2 +1)^2 ))dx=

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{2}{x}^{\mathrm{2}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}= \\ $$

Question Number 154927 Answers: 1 Comments: 0

Let I_n =∫x^n e^(−x) dx show that ∫_0 ^∞ x^n e^(−x) dx=n!

$$\mathrm{Let}\:{I}_{{n}} =\int{x}^{{n}} {e}^{−{x}} {dx} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{{n}} {e}^{−{x}} {dx}={n}! \\ $$

Question Number 154880 Answers: 6 Comments: 0

Question Number 154877 Answers: 2 Comments: 1

∫_(π/2) ^(π/4) sin^3 (x)cos^2 (x)dx

$$\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{4}}} {sin}^{\mathrm{3}} \left({x}\right){cos}^{\mathrm{2}} \left({x}\right){dx} \\ $$

Question Number 154876 Answers: 1 Comments: 0

Integrate: ∫_1 ^( 8) (( (√x)−x^2 )/( ^3 (√x))) dx

$$\:\:\boldsymbol{\mathrm{Integrate}}: \\ $$$$\:\:\:\int_{\mathrm{1}} ^{\:\mathrm{8}} \:\:\frac{\:\sqrt{\boldsymbol{\mathrm{x}}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\overset{\mathrm{3}} {\:}\sqrt{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 154875 Answers: 1 Comments: 0

Question Number 154872 Answers: 1 Comments: 0

∫_(−∞) ^( ∞) sin(x^3 )cos(x^4 )dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \mathrm{sin}\left({x}^{\mathrm{3}} \right)\mathrm{cos}\left({x}^{\mathrm{4}} \right){dx} \\ $$$$\: \\ $$

Question Number 154910 Answers: 1 Comments: 2

Question Number 154860 Answers: 0 Comments: 0

(1/(n+1))+(1/(n+2))+(1/(n+3))+...+(1/(2n))<(3/4) n>1 Prove that

$$\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}+...+\frac{\mathrm{1}}{\mathrm{2n}}<\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{n}>\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$

Question Number 154857 Answers: 1 Comments: 0

Question Number 154854 Answers: 1 Comments: 1

Question Number 154853 Answers: 1 Comments: 0

Question Number 154851 Answers: 0 Comments: 7

Question Number 154849 Answers: 1 Comments: 0

ax + y + z = 1 x + ay + z = a x + y + az = a^2 Find value of x, y, z in a .

$${ax}\:+\:{y}\:+\:{z}\:=\:\mathrm{1} \\ $$$${x}\:+\:{ay}\:+\:{z}\:=\:{a} \\ $$$${x}\:+\:{y}\:+\:{az}\:=\:{a}^{\mathrm{2}} \\ $$$${Find}\:\:{value}\:\:{of}\:\:{x},\:{y},\:{z}\:\:\:{in}\:\:{a}\:. \\ $$

Question Number 154846 Answers: 0 Comments: 2

y′=((y cos(x))/(1+2y^2 )) trouve la solution de lequation differentielle

$${y}'=\frac{{y}\:{cos}\left({x}\right)}{\mathrm{1}+\mathrm{2}{y}^{\mathrm{2}} } \\ $$$${trouve}\:{la}\:{solution}\:{de}\:{lequation}\:{differentielle} \\ $$

Question Number 154823 Answers: 1 Comments: 0

∫_0 ^( ∞) (e^(−x) /( x^(3/4) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{e}^{−{x}} }{\:{x}^{\frac{\mathrm{3}}{\mathrm{4}}} \:}\:{dx} \\ $$$$\: \\ $$

Question Number 154824 Answers: 1 Comments: 0

Σ_(k=0) ^∞ ((4^(−k) Γ(k))/(k!))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{−{k}} \Gamma\left({k}\right)}{{k}!} \\ $$$$\: \\ $$

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