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Question Number 144929 Answers: 1 Comments: 0

find the value lim_(n→∞) (1+((1+(1/2)+(1/3)+(1/4)+...+(1/n))/n^2 ))^n

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+...+\frac{\mathrm{1}}{\mathrm{n}}}{\mathrm{n}^{\mathrm{2}} }\right)^{\mathrm{n}} \:\: \\ $$

Question Number 144928 Answers: 1 Comments: 0

Σ_(n≥0) (((−1)^n )/((n+z)n!))

$$\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+{z}\right){n}!} \\ $$

Question Number 144926 Answers: 1 Comments: 0

∫_0 ^∞ x^n (e^(ix) )^z dx=??? (z∈C)

$$\int_{\mathrm{0}} ^{\infty} {x}^{{n}} \left({e}^{{ix}} \right)^{{z}} {dx}=???\:\:\:\left({z}\in\mathbb{C}\right) \\ $$

Question Number 144925 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (((2n)!!)/(2^n ∙(n+1)∙(2n+1)!!))=?

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\mathrm{2}^{\mathrm{n}} \centerdot\left(\mathrm{n}+\mathrm{1}\right)\centerdot\left(\mathrm{2n}+\mathrm{1}\right)!!}=? \\ $$

Question Number 144924 Answers: 1 Comments: 0

S(x)=Σ_(n=1) ^∞ (((2n)!!)/((2n+1)!!))x^(2n) =?........(∣x∣<1)

$$\mathrm{S}\left(\mathrm{x}\right)=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!}\mathrm{x}^{\mathrm{2n}} =?........\left(\mid\mathrm{x}\mid<\mathrm{1}\right) \\ $$

Question Number 144922 Answers: 1 Comments: 0

if z^2 - 16(√z) = 12 find z - 2(√z) = ?

$${if}\:\:{z}^{\mathrm{2}} \:-\:\mathrm{16}\sqrt{{z}}\:=\:\mathrm{12} \\ $$$${find}\:\:{z}\:-\:\mathrm{2}\sqrt{{z}}\:=\:? \\ $$

Question Number 144917 Answers: 1 Comments: 0

if x;y>0 then: 10 ∙ (√((x^2 +y^2 )/2)) + ((8xy)/(x+y)) ≥ 7x+7y

$${if}\:\:{x};{y}>\mathrm{0}\:\:{then}: \\ $$$$\mathrm{10}\:\centerdot\:\sqrt{\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\mathrm{2}}}\:+\:\frac{\mathrm{8}{xy}}{{x}+{y}}\:\geqslant\:\mathrm{7}{x}+\mathrm{7}{y} \\ $$

Question Number 144914 Answers: 2 Comments: 0

If ((1+tan 4(√θ))/(1−tan 4(√θ))) = tan θ , then find possible value of tan (θ+11(√θ) ).

$$\:\mathrm{If}\:\frac{\mathrm{1}+\mathrm{tan}\:\mathrm{4}\sqrt{\theta}}{\mathrm{1}−\mathrm{tan}\:\mathrm{4}\sqrt{\theta}}\:=\:\mathrm{tan}\:\theta\:,\:\mathrm{then}\:\mathrm{find}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\theta+\mathrm{11}\sqrt{\theta}\:\right). \\ $$

Question Number 144910 Answers: 0 Comments: 0

Γ(((n+1)/(1−i)))=????

$$\Gamma\left(\frac{{n}+\mathrm{1}}{\mathrm{1}−{i}}\right)=???? \\ $$

Question Number 144909 Answers: 1 Comments: 0

Γ(a+ib) doesn′t exist ? give her value

$$\Gamma\left({a}+{ib}\right)\:{doesn}'{t}\:{exist}\:?\:{give}\:{her}\:{value} \\ $$

Question Number 144903 Answers: 0 Comments: 0

Question Number 144900 Answers: 1 Comments: 0

etude complete de la courbe d′equation polaire r=(1/(sin(2θ))) (symetrie et trace)

$${etude}\:{complete}\:{de}\:{la}\:{courbe}\:{d}'{equation} \\ $$$${polaire}\:{r}=\frac{\mathrm{1}}{{sin}\left(\mathrm{2}\theta\right)}\:\:\:\:\left({symetrie}\:{et}\:{trace}\right) \\ $$$$ \\ $$

Question Number 144899 Answers: 0 Comments: 0

Ω := ∫ ((√(1−sin(x)))/(cos (x))) e^(−(1/2) x) = ?

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\Omega\::=\:\int\:\frac{\sqrt{\mathrm{1}−{sin}\left({x}\right)}}{{cos}\:\left({x}\right)}\:{e}\:^{−\frac{\mathrm{1}}{\mathrm{2}}\:{x}} =\:? \\ $$$$ \\ $$

Question Number 144897 Answers: 0 Comments: 0

∫_0 ^(([x])/3) (8^x /2^([3x]) ) dx= ??? where [.] is the greatest integer function.

$$\underset{\mathrm{0}} {\overset{\frac{\left[{x}\right]}{\mathrm{3}}} {\int}}\frac{\mathrm{8}^{{x}} }{\mathrm{2}^{\left[\mathrm{3}{x}\right]} }\:{dx}=\:???\:\mathrm{where}\:\left[.\right]\:\mathrm{is}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}. \\ $$

Question Number 144896 Answers: 1 Comments: 0

Evaluate ∫e^x (((1−x)/(1+x^2 )))^2 dx

$$\mathrm{Evaluate}\: \\ $$$$\:\int{e}^{{x}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} {dx}\: \\ $$

Question Number 144890 Answers: 1 Comments: 1

Question Number 144888 Answers: 2 Comments: 1

Question Number 144887 Answers: 1 Comments: 0

Question Number 144905 Answers: 0 Comments: 1

Question Number 144877 Answers: 1 Comments: 0

u+(√u)+(u)^(1/3) +(u)^(1/4) +(u)^(1/5) +... +∞=?

$$\:\:\mathrm{u}+\sqrt{\mathrm{u}}+\sqrt[{\mathrm{3}}]{\mathrm{u}}+\sqrt[{\mathrm{4}}]{\mathrm{u}}+\sqrt[{\mathrm{5}}]{\mathrm{u}}+...\:+\infty=? \\ $$$$ \\ $$

Question Number 144872 Answers: 0 Comments: 0

Question Number 144869 Answers: 1 Comments: 0

if 3^z = (1/(3^(5(√3)) ∙ 3^2 )) find z=?

$${if}\:\:\mathrm{3}^{\boldsymbol{{z}}} \:=\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{5}\sqrt{\mathrm{3}}} \:\centerdot\:\mathrm{3}^{\mathrm{2}} }\:\:{find}\:\:\boldsymbol{{z}}=? \\ $$

Question Number 144901 Answers: 0 Comments: 0

Let a,b > 0 and a+b+1 = 3ab. Prove that (a/(a^2 +1))+(b/(b^2 +1)) ≤ 1 ≤ (a^3 /(a^2 +1))+(b^3 /(b^2 +1)) Let a,b > 0, n ∈ Z^+ and a+b+1 = 3ab. Prove or disprove (a^(n−1) /(a^n +1))+(b^(n−1) /(b^n +1)) ≤ 1 ≤ (a^(n+1) /(a^n +1))+(b^(n+1) /(b^n +1))

$$\mathrm{Let}\:{a},{b}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+\mathrm{1}\:=\:\mathrm{3}{ab}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}}{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{b}}{{b}^{\mathrm{2}} +\mathrm{1}}\:\leqslant\:\mathrm{1}\:\leqslant\:\frac{{a}^{\mathrm{3}} }{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{b}^{\mathrm{3}} }{{b}^{\mathrm{2}} +\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Let}\:{a},{b}\:>\:\mathrm{0},\:{n}\:\in\:\mathbb{Z}^{+} \:\mathrm{and}\:{a}+{b}+\mathrm{1}\:=\:\mathrm{3}{ab}.\:\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{{n}−\mathrm{1}} }{{a}^{{n}} +\mathrm{1}}+\frac{{b}^{{n}−\mathrm{1}} }{{b}^{{n}} +\mathrm{1}}\:\leqslant\:\mathrm{1}\:\leqslant\:\frac{{a}^{{n}+\mathrm{1}} }{{a}^{{n}} +\mathrm{1}}+\frac{{b}^{{n}+\mathrm{1}} }{{b}^{{n}} +\mathrm{1}} \\ $$$$ \\ $$

Question Number 144860 Answers: 0 Comments: 2

∣(x/(x-1))∣ + ∣x∣ = (x^2 /(∣x-1∣)) find x=?

$$\mid\frac{{x}}{{x}-\mathrm{1}}\mid\:+\:\mid{x}\mid\:=\:\frac{{x}^{\mathrm{2}} }{\mid{x}-\mathrm{1}\mid}\:\:\:{find}\:\:{x}=? \\ $$

Question Number 144858 Answers: 1 Comments: 0

Question Number 144857 Answers: 0 Comments: 0

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