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Question Number 146009    Answers: 1   Comments: 0

(1/4)+(1/(12))+(1/(24))+...+(1/(2n(n+1)))=?

$$\:\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{12}}+\frac{\mathrm{1}}{\mathrm{24}}+...+\frac{\mathrm{1}}{\mathrm{2n}\left(\mathrm{n}+\mathrm{1}\right)}=? \\ $$

Question Number 146004    Answers: 1   Comments: 0

F et G deux sous espaces vectoriels de E a) montrer que (F∩G=F+G)⇔(F=G) b) quand dit−on que les deux sous espaces vectoriels F et G sont supplementaires?

$$\mathrm{F}\:\mathrm{et}\:\mathrm{G}\:\mathrm{deux}\:\mathrm{sous}\:\mathrm{espaces}\:\mathrm{vectoriels}\:\mathrm{de}\:\mathrm{E} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{montrer}\:\mathrm{que}\:\left(\mathrm{F}\cap\mathrm{G}=\mathrm{F}+\mathrm{G}\right)\Leftrightarrow\left(\mathrm{F}=\mathrm{G}\right) \\ $$$$\left.\mathrm{b}\right)\:\mathrm{quand}\:\mathrm{dit}−\mathrm{on}\:\mathrm{que}\:\mathrm{les}\:\mathrm{deux}\:\mathrm{sous}\:\mathrm{espaces}\: \\ $$$$\mathrm{vectoriels}\:\mathrm{F}\:\mathrm{et}\:\mathrm{G}\:\mathrm{sont}\:\mathrm{supplementaires}? \\ $$

Question Number 145996    Answers: 3   Comments: 0

find the sum of x−2x^2 +3x^3 −4x^4 +5x^5 −6x^6 +... where ∣x∣ < 1

$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\: \\ $$$$\:\mathrm{x}−\mathrm{2x}^{\mathrm{2}} +\mathrm{3x}^{\mathrm{3}} −\mathrm{4x}^{\mathrm{4}} +\mathrm{5x}^{\mathrm{5}} −\mathrm{6x}^{\mathrm{6}} +... \\ $$$$\mathrm{where}\:\mid\mathrm{x}\mid\:<\:\mathrm{1} \\ $$

Question Number 148416    Answers: 1   Comments: 0

lim_(x→∞) ((x! - cos(2x))/(3x + 1)) = ?

$$\underset{\boldsymbol{{x}}\rightarrow\infty} {{lim}}\frac{{x}!\:-\:{cos}\left(\mathrm{2}{x}\right)}{\mathrm{3}{x}\:+\:\mathrm{1}}\:=\:? \\ $$

Question Number 145986    Answers: 1   Comments: 0

What is x−f(x)×e/3.5π×θ=??????? function f(input) = decrypt( determinant ((( determinant (( )) )))

$${What}\:{is} \\ $$$${x}−{f}\left({x}\right)×{e}/\mathrm{3}.\mathrm{5}\pi×\theta=??????? \\ $$$${function}\:{f}\left({input}\right)\:=\:{decrypt}\left(\begin{array}{|c|}{\begin{array}{|c|}{\underbrace{ }}\\\hline\end{array}\underbrace{ }}\\\hline\end{array}\right. \\ $$

Question Number 145982    Answers: 1   Comments: 0

Σ_(n≥0) (−(1/(81)))^n Γ(3n+3)=??

$$\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\frac{\mathrm{1}}{\mathrm{81}}\right)^{{n}} \Gamma\left(\mathrm{3}{n}+\mathrm{3}\right)=?? \\ $$

Question Number 145981    Answers: 0   Comments: 0

let f(x) be a function period 2π such that:f(x)={x, 0<x<π {π, π<x<2π show that the fourier series for f(x) in the interval 0<x<2π is ((3π)/4)−(2/π)[cosx+(1/3^2 )cos3x+(1/5^2 )cos5x+...]−[sinx+(1/2)sin2x+(1/3)sin3x+...]

$${let}\:{f}\left({x}\right)\:{be}\:{a}\:{function}\:{period}\:\mathrm{2}\pi\:{such}\:{that}:{f}\left({x}\right)=\left\{{x},\:\mathrm{0}<{x}<\pi\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{\pi,\:\pi<{x}<\mathrm{2}\pi\right. \\ $$$${show}\:{that}\:{the}\:{fourier}\:{series}\:{for}\:{f}\left({x}\right)\:{in}\:{the}\:{interval}\:\mathrm{0}<{x}<\mathrm{2}\pi\:{is} \\ $$$$\frac{\mathrm{3}\pi}{\mathrm{4}}−\frac{\mathrm{2}}{\pi}\left[{cosx}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }{cos}\mathrm{3}{x}+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }{cos}\mathrm{5}{x}+...\right]−\left[{sinx}+\frac{\mathrm{1}}{\mathrm{2}}{sin}\mathrm{2}{x}+\frac{\mathrm{1}}{\mathrm{3}}{sin}\mathrm{3}{x}+...\right] \\ $$

Question Number 145979    Answers: 1   Comments: 0

sin^2 x−4cos^3 x−1=2cos^2 x+2cos x−2cos xsin^2 x x=?

$$\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{4cos}\:^{\mathrm{3}} \mathrm{x}−\mathrm{1}=\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{2cos}\:\mathrm{x}−\mathrm{2cos}\:\mathrm{xsin}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\mathrm{x}=? \\ $$

Question Number 145975    Answers: 1   Comments: 0

∫_( 0) ^( 6) [ (√(36−x^2 ))−(6−x)]dx=?

$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{6}} {\int}}\:\left[\:\sqrt{\mathrm{36}−{x}^{\mathrm{2}} }−\left(\mathrm{6}−{x}\right)\right]{dx}=? \\ $$

Question Number 146001    Answers: 1   Comments: 0

Soit p∈End(E). on pose q=id_E −p a) montrer que p est un projecteur si et seulement si q est un projecteur.. b) on suppose que p est un projecteur et on considere L={f∈End(E)/∃u∈End(E),f=u○p} et M={g∈End(E)/∃v∈End(E), g=v○q}. montrer que L et M sont des sous espaces vectoriels supplementaires de End(E)..

$$\mathrm{Soit}\:\mathrm{p}\in\mathrm{End}\left(\mathrm{E}\right).\:\mathrm{on}\:\mathrm{pose}\:\mathrm{q}=\mathrm{id}_{\mathrm{E}} −\mathrm{p} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{montrer}\:\mathrm{que}\:\mathrm{p}\:\mathrm{est}\:\mathrm{un}\:\mathrm{projecteur}\:\mathrm{si}\:\mathrm{et}\: \\ $$$$\mathrm{seulement}\:\mathrm{si}\:\mathrm{q}\:\mathrm{est}\:\mathrm{un}\:\mathrm{projecteur}.. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{on}\:\mathrm{suppose}\:\mathrm{que}\:\mathrm{p}\:\mathrm{est}\:\mathrm{un}\:\mathrm{projecteur}\:\mathrm{et}\:\mathrm{on} \\ $$$$\mathrm{considere}\:\mathrm{L}=\left\{\mathrm{f}\in\mathrm{End}\left(\mathrm{E}\right)/\exists\mathrm{u}\in\mathrm{End}\left(\mathrm{E}\right),\mathrm{f}=\mathrm{u}\circ\mathrm{p}\right\} \\ $$$$\mathrm{et}\:\mathrm{M}=\left\{\mathrm{g}\in\mathrm{End}\left(\mathrm{E}\right)/\exists\mathrm{v}\in\mathrm{End}\left(\mathrm{E}\right),\:\mathrm{g}=\mathrm{v}\circ\mathrm{q}\right\}. \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{L}\:\mathrm{et}\:\mathrm{M}\:\mathrm{sont}\:\mathrm{des}\:\mathrm{sous}\:\mathrm{espaces}\: \\ $$$$\mathrm{vectoriels}\:\mathrm{supplementaires}\:\mathrm{de}\:\mathrm{End}\left(\mathrm{E}\right).. \\ $$

Question Number 146000    Answers: 0   Comments: 3

Question Number 145960    Answers: 2   Comments: 0

Question Number 145954    Answers: 1   Comments: 0

1+i+i^2 +i^3 +...+i^(99) =?

$$\mathrm{1}+{i}+{i}^{\mathrm{2}} +{i}^{\mathrm{3}} +...+{i}^{\mathrm{99}} =? \\ $$

Question Number 145953    Answers: 1   Comments: 4

Question Number 145951    Answers: 1   Comments: 0

Σ_(n≥1) (((−1)^n )/n)=??

$$\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}=?? \\ $$

Question Number 145947    Answers: 1   Comments: 1

Question Number 145946    Answers: 1   Comments: 0

the type of singular point of f(z)=((cos(πz))/((1−z^3 ))) is ?

$${the}\:{type}\:{of}\:{singular}\:{point}\:{of}\:{f}\left({z}\right)=\frac{{cos}\left(\pi{z}\right)}{\left(\mathrm{1}−{z}^{\mathrm{3}} \right)}\:{is}\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 145944    Answers: 1   Comments: 1

Question Number 145942    Answers: 1   Comments: 0

Question Number 145941    Answers: 1   Comments: 0

find ∫_0 ^∞ e^(−3x) log(1+x^3 )dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{3}{x}} {log}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$

Question Number 145940    Answers: 0   Comments: 0

find ∫_0 ^1 e^(−x) log(1−x^4 )dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {log}\left(\mathrm{1}−{x}^{\mathrm{4}} \right){dx} \\ $$

Question Number 145939    Answers: 0   Comments: 0

Ψ(x)=ch(sinx) developp Ψ at fourier serie

$$\Psi\left({x}\right)={ch}\left({sinx}\right) \\ $$$${developp}\:\Psi\:{at}\:{fourier}\:{serie} \\ $$

Question Number 145938    Answers: 1   Comments: 0

g(x)=cos(arctanx) if g(x)=Σ a_n x^n determine the sequence a_n

$${g}\left({x}\right)={cos}\left({arctanx}\right) \\ $$$${if}\:{g}\left({x}\right)=\Sigma\:{a}_{{n}} {x}^{{n}} \:{determine}\:{the} \\ $$$${sequence}\:{a}_{{n}} \\ $$

Question Number 145936    Answers: 0   Comments: 0

g(x)=arctan(cosx) developp f at fourier serie

$${g}\left({x}\right)={arctan}\left({cosx}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 145934    Answers: 0   Comments: 0

Question Number 145918    Answers: 1   Comments: 0

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