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Question Number 196327 Answers: 2 Comments: 0

calcul la somme suivante: lim_(n→+∞) Σ_(k=n) ^(2n) sin((𝛑/k)) elrochi

$$\boldsymbol{{calcul}}\:\boldsymbol{{la}}\:\boldsymbol{{somme}}\:\boldsymbol{{suivante}}: \\ $$$$\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow+\infty} {\boldsymbol{{m}}}\:\underset{\boldsymbol{{k}}=\boldsymbol{{n}}} {\overset{\mathrm{2}\boldsymbol{{n}}} {\sum}}\boldsymbol{{sin}}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{{k}}}\right) \\ $$$$\:\:\boldsymbol{{elrochi}} \\ $$

Question Number 196325 Answers: 1 Comments: 0

Σ_(n=0) ^∞ arg(n^2 +n+1+i)= π/2

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)=\:\pi/\mathrm{2}\: \\ $$

Question Number 196324 Answers: 2 Comments: 0

Question Number 196322 Answers: 1 Comments: 0

f^((1/2)) (x)= (d/dx)(∫_0 ^x ((f(x−t))/( (√(πt))))dt) Prove that (f^((1/2)) )^((1/2)) = f ′ At least for f = 1 then f = x

$$\:\:\:\:{f}^{\left(\mathrm{1}/\mathrm{2}\right)} \left({x}\right)=\:\frac{{d}}{{dx}}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{f}\left({x}−{t}\right)}{\:\sqrt{\pi{t}}}{dt}\right) \\ $$$${Prove}\:\:{that}\:\:\:\:\left({f}^{\left(\mathrm{1}/\mathrm{2}\right)} \right)^{\left(\mathrm{1}/\mathrm{2}\right)} =\:{f}\:'\:\:\:\: \\ $$$${At}\:\:{least}\:\:{for}\:\:{f}\:=\:\:\mathrm{1}\:\:{then}\:\:{f}\:=\:{x} \\ $$

Question Number 196321 Answers: 1 Comments: 0

lim_(n→+∞) sin(2π(√(n^2 +1 )) ) = 0 lim_(n→+∞) arg(n^2 +n+1+i) = 0

$$\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{sin}\left(\mathrm{2}\pi\sqrt{{n}^{\mathrm{2}} +\mathrm{1}\:}\:\right)\:=\:\mathrm{0} \\ $$$$\:\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:\:{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)\:=\:\mathrm{0} \\ $$

Question Number 196320 Answers: 1 Comments: 0

If a regular n−polygon can be divided into n identical equilateral triangles then n=6

$$\:\:{If}\:\:{a}\:\:{regular}\:{n}−{polygon}\:{can} \\ $$$$\:{be}\:{divided}\:{into}\:\:{n}\:\:{identical}\:\: \\ $$$${equilateral}\:{triangles}\:{then}\:\:{n}=\mathrm{6} \\ $$

Question Number 196311 Answers: 0 Comments: 0

Question Number 196309 Answers: 2 Comments: 1

Question Number 196304 Answers: 3 Comments: 0

Question Number 196303 Answers: 2 Comments: 0

Question Number 196302 Answers: 1 Comments: 0

Question Number 196300 Answers: 2 Comments: 0

If → n ∈ N and n ≥ 2 Then → tan ((1/(n − 1)) Σ_(k=2) ^n arctan (1/k)) < (2/5) + (𝛄/(n − 1))

$$\mathrm{If}\:\rightarrow\:\mathrm{n}\:\in\:\mathbb{N}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{n}\:\geqslant\:\mathrm{2} \\ $$$$\mathrm{Then}\:\rightarrow\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{n}\:−\:\mathrm{1}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{2}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{k}}\right)\:<\:\frac{\mathrm{2}}{\mathrm{5}}\:+\:\frac{\boldsymbol{\gamma}}{\mathrm{n}\:−\:\mathrm{1}} \\ $$

Question Number 196299 Answers: 1 Comments: 0

If → y = x ! find → (dy/dx)

$$\mathrm{If}\:\rightarrow\:\mathrm{y}\:=\:\mathrm{x}\:!\:\:\:\:\:\mathrm{find}\:\rightarrow\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$

Question Number 196298 Answers: 0 Comments: 0

Q#196258 (please)

$${Q}#\mathrm{196258}\:\left({please}\right) \\ $$

Question Number 196288 Answers: 3 Comments: 1

4^x =(√5^y )=400 ((xy)/(2x+y))=?

$$\mathrm{4}^{{x}} =\sqrt{\mathrm{5}^{{y}} }=\mathrm{400} \\ $$$$\frac{{xy}}{\mathrm{2}{x}+{y}}=? \\ $$

Question Number 196286 Answers: 0 Comments: 0

Question Number 196285 Answers: 0 Comments: 1

problem 196258 (please)

$${problem}\:\mathrm{196258}\:\left({please}\right) \\ $$

Question Number 196277 Answers: 3 Comments: 0

(d^2 /dy^2 ) (sin^3 x) =?

$$\:\:\:\: \\ $$$$ \:\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dy}^{\mathrm{2}} }\:\left(\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}\right)\:=?\: \\ $$

Question Number 196276 Answers: 1 Comments: 0

Question Number 196275 Answers: 1 Comments: 0

Question Number 196267 Answers: 1 Comments: 2

if lim_(n→+∞) (1+ (x/(7n)))^(29n) =2023 find x ??

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:{if}\:\:\:{lim}_{{n}\rightarrow+\infty} \:\left(\mathrm{1}+\:\frac{{x}}{\mathrm{7}{n}}\right)^{\mathrm{29}{n}} =\mathrm{2023} \\ $$$$\:\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{{x}}\:?? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 196265 Answers: 2 Comments: 0

Question Number 196261 Answers: 1 Comments: 0

Question Number 196258 Answers: 0 Comments: 4

If(x_m +iy_m )^(2n+1) =1 , such that m∈{1,2,3,....,2n} ∧ x_m ,y_m ∈R p=Σ_(k=1) ^(2020) [((1−x_k +iy_k )/(1+x_k +iy_k ))] , Find ((p/(43)))

$${If}\left({x}_{{m}} +{iy}_{{m}} \right)^{\mathrm{2}{n}+\mathrm{1}} =\mathrm{1}\:,\:{such}\:{that} \\ $$$${m}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},....,\mathrm{2}{n}\right\}\:\wedge\:{x}_{{m}} ,{y}_{{m}} \in\mathbb{R} \\ $$$${p}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2020}} {\sum}}\left[\frac{\mathrm{1}−{x}_{{k}} +{iy}_{{k}} }{\mathrm{1}+{x}_{{k}} +{iy}_{{k}} }\right]\:,\:{Find}\:\left(\frac{{p}}{\mathrm{43}}\right) \\ $$

Question Number 196257 Answers: 1 Comments: 0

Question Number 197581 Answers: 1 Comments: 0

find Σ_(n=1) ^k (√n) ?

$${find}\:\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\sqrt{{n}}\:? \\ $$

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