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Question Number 120480 Answers: 4 Comments: 0

show that ∀ n ∈N^∗ Σ_(k=1) ^n k(n−k)=(((n−1)(n+1))/6)

$${show}\:{that}\:\forall\:{n}\:\in\mathbb{N}^{\ast} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}} {k}\left({n}−{k}\right)=\frac{\left({n}−\mathrm{1}\right)\left({n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$

Question Number 120477 Answers: 2 Comments: 0

Question Number 120475 Answers: 1 Comments: 0

Question Number 120472 Answers: 0 Comments: 0

A=5x23^(−) ^6 show that A≡x−4[7] deduct the value of x for which A is divisible by 7

$${A}=\overline {\mathrm{5}{x}\mathrm{23}}\:^{\mathrm{6}} \:{show}\:{that}\:{A}\equiv{x}−\mathrm{4}\left[\mathrm{7}\right] \\ $$$${deduct}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{A}\:{is}\: \\ $$$${divisible}\:{by}\:\mathrm{7} \\ $$

Question Number 120471 Answers: 1 Comments: 0

solve in Z x^3 +2x+1≡1[4]

$${solve}\:{in}\:\mathbb{Z}\:{x}^{\mathrm{3}} +\mathrm{2}{x}+\mathrm{1}\equiv\mathrm{1}\left[\mathrm{4}\right] \\ $$

Question Number 120470 Answers: 0 Comments: 0

solve in function of n: 2^n ≡x−4[3] n∈N

$${solve}\:{in}\:{function}\:{of}\:{n}: \\ $$$$\mathrm{2}^{{n}} \equiv{x}−\mathrm{4}\left[\mathrm{3}\right] \\ $$$${n}\in\mathbb{N} \\ $$

Question Number 120469 Answers: 1 Comments: 0

c alculate the rest of the division of 2^n by 3 ; n ∈ N

$${c}\:{alculate}\:{the}\:{rest}\:{of}\:{the}\:{division}\:{of} \\ $$$$\mathrm{2}^{{n}} \:{by}\:\mathrm{3}\:;\:{n}\:\in\:\mathbb{N} \\ $$

Question Number 120468 Answers: 0 Comments: 2

Question Number 120467 Answers: 1 Comments: 0

Question Number 120464 Answers: 1 Comments: 0

Question Number 120463 Answers: 2 Comments: 0

Find the slope of the line tangent to the graph r=3cos^2 (2θ) at θ=(π/6).

$${Find}\:{the}\:{slope}\:{of}\:{the}\:{line}\:{tangent} \\ $$$${to}\:{the}\:{graph}\:{r}=\mathrm{3cos}\:^{\mathrm{2}} \left(\mathrm{2}\theta\right)\:{at} \\ $$$$\theta=\frac{\pi}{\mathrm{6}}.\: \\ $$

Question Number 120461 Answers: 1 Comments: 0

∫sin(lnx)dx

$$\int\mathrm{sin}\left(\mathrm{ln}{x}\right){dx} \\ $$

Question Number 120459 Answers: 0 Comments: 1

Question Number 120455 Answers: 0 Comments: 0

Question Number 120452 Answers: 2 Comments: 0

Find the equation of the line tangent to the parametric curve given by the equations { ((x=(1+t^3 )^4 +t^2 )),((y=t^5 +t^2 +2)) :} at t=1

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{tangent}\:{to}\:{the}\:{parametric} \\ $$$${curve}\:{given}\:{by}\:{the}\:{equations}\:\begin{cases}{{x}=\left(\mathrm{1}+{t}^{\mathrm{3}} \right)^{\mathrm{4}} +{t}^{\mathrm{2}} }\\{{y}={t}^{\mathrm{5}} +{t}^{\mathrm{2}} +\mathrm{2}}\end{cases}\:{at}\:{t}=\mathrm{1} \\ $$

Question Number 120445 Answers: 1 Comments: 0

Question Number 120444 Answers: 0 Comments: 0

Question Number 120438 Answers: 3 Comments: 0

Question Number 120431 Answers: 1 Comments: 2

Question Number 120427 Answers: 2 Comments: 0

lim_(x→0) (((√(cos x+(√(2sin x+x)))) −1)/(sin x))

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{cos}\:{x}+\sqrt{\mathrm{2sin}\:{x}+{x}}}\:−\mathrm{1}}{\mathrm{sin}\:{x}} \\ $$

Question Number 120425 Answers: 4 Comments: 0

lim_(x→0) ((2^x −cos x)/(sin x)) ?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{{x}} −\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}\:? \\ $$

Question Number 120422 Answers: 0 Comments: 4

Question Number 120414 Answers: 0 Comments: 0

Question Number 120413 Answers: 1 Comments: 1

Question Number 120409 Answers: 3 Comments: 1

I/.∫((1/(lnx)) − (1/(ln^2 x)))dx (Helpe me please)

$$\mathrm{I}/.\int\left(\frac{\mathrm{1}}{\mathrm{lnx}}\:−\:\frac{\mathrm{1}}{\mathrm{ln}^{\mathrm{2}} \mathrm{x}}\right)\mathrm{dx} \\ $$$$\left(\mathrm{Helpe}\:\mathrm{me}\:\mathrm{please}\right) \\ $$

Question Number 120395 Answers: 3 Comments: 0

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