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Question Number 166520 Answers: 2 Comments: 2

Question Number 166516 Answers: 0 Comments: 0

Determine the formula of this expression Σ_(k=0) ^n (1/((n−k)!(n+k)!))

$$\mathrm{Determine}\:\:\mathrm{the}\:\:\mathrm{formula}\:\:\mathrm{of}\:\:\mathrm{this}\:\:\mathrm{expression} \\ $$$$\:\:\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\left({n}−{k}\right)!\left({n}+{k}\right)!}\: \\ $$

Question Number 166515 Answers: 1 Comments: 0

Given a function (x+1)f(−x)+((1−x)/(4x)) f((1/x))=((100(x^2 +4))/x) x≠0 , x≠1 Find f(2)+f(3)+f(4)+...+f(400)

$$\:\:\:\:{Given}\:{a}\:{function}\: \\ $$$$\:\:\:\left({x}+\mathrm{1}\right){f}\left(−{x}\right)+\frac{\mathrm{1}−{x}}{\mathrm{4}{x}}\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{100}\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{{x}} \\ $$$$\:{x}\neq\mathrm{0}\:,\:{x}\neq\mathrm{1} \\ $$$$\:{Find}\:{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{4}\right)+...+{f}\left(\mathrm{400}\right) \\ $$

Question Number 166511 Answers: 1 Comments: 0

is the function f(x) = tan^(−1) (x) + tan^(−1) (2x) + tan^(−1) (3x) + ..... converge or diverge ?

$${is}\:{the}\:{function}\:{f}\left({x}\right)\:=\:{tan}^{−\mathrm{1}} \left({x}\right)\:+\:{tan}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)\:+\:{tan}^{−\mathrm{1}} \left(\mathrm{3}{x}\right)\:+\:.....\: \\ $$$${converge}\:{or}\:{diverge}\:? \\ $$$$ \\ $$

Question Number 166496 Answers: 0 Comments: 1

Calculas: ((2 (√6))/( (√5) + (√3) + (√2))) - (1/( (√3) - (√2))) = ?

$$\mathrm{Calculas}: \\ $$$$\frac{\mathrm{2}\:\sqrt{\mathrm{6}}}{\:\sqrt{\mathrm{5}}\:+\:\sqrt{\mathrm{3}}\:+\:\sqrt{\mathrm{2}}}\:-\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}\:-\:\sqrt{\mathrm{2}}}\:=\:? \\ $$

Question Number 166491 Answers: 0 Comments: 4

Question Number 166488 Answers: 1 Comments: 0

B=∫ (√((sin 2x−1)/(cos 2x−1))) dx =?

$$\:\:\:\mathrm{B}=\int\:\sqrt{\frac{\mathrm{sin}\:\mathrm{2x}−\mathrm{1}}{\mathrm{cos}\:\mathrm{2x}−\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$

Question Number 166481 Answers: 2 Comments: 1

Question Number 166480 Answers: 0 Comments: 0

Question Number 166475 Answers: 2 Comments: 5

Find out n∈N such that n^2 +n is divisible by 30.

$$\mathcal{F}{ind}\:{out}\:{n}\in\mathbb{N} \\ $$$$\:{such}\:{that} \\ $$$${n}^{\mathrm{2}} +{n}\:{is}\:{divisible}\:{by}\:\mathrm{30}. \\ $$

Question Number 166468 Answers: 2 Comments: 0

1+3(√2)x−18x^2 =6x(√(1−9x^2 )) solve in R

$$\mathrm{1}+\mathrm{3}\sqrt{\mathrm{2}}{x}−\mathrm{18}{x}^{\mathrm{2}} =\mathrm{6}{x}\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} } \\ $$$${solve}\:\:{in}\:{R} \\ $$

Question Number 166465 Answers: 1 Comments: 1

Question Number 166449 Answers: 1 Comments: 3

C = ∫ ((1−tan^2 x)/(1+sec^2 x)) dx =?

$$\:\:\:\mathrm{C}\:=\:\int\:\frac{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{1}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 166448 Answers: 0 Comments: 2

montrer q ∀nεN n^2 +n est divisible par 30

$${montrer}\:{q}\:\:\forall{n}\epsilon{N} \\ $$$${n}^{\mathrm{2}} +{n}\:{est}\:{divisible}\:{par}\:\mathrm{30} \\ $$

Question Number 166443 Answers: 2 Comments: 1

fog_((3)) =10 f(3)=4 g(x)=?

$${fog}_{\left(\mathrm{3}\right)} =\mathrm{10} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{4} \\ $$$${g}\left({x}\right)=? \\ $$

Question Number 166442 Answers: 2 Comments: 0

Question Number 166440 Answers: 0 Comments: 1

Question Number 166437 Answers: 1 Comments: 0

calculate Ω=∫_0 ^( 1) (( ln(1−x ).ln(1+ x ))/x^( 2) ) dx=? −−−−−−−

$$ \\ $$$$\:\:\:\:\:\:{calculate}\: \\ $$$$\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:{ln}\left(\mathrm{1}−{x}\:\right).{ln}\left(\mathrm{1}+\:{x}\:\right)}{{x}^{\:\mathrm{2}} }\:{dx}=? \\ $$$$\:\:\:\:\:\:−−−−−−− \\ $$

Question Number 166436 Answers: 2 Comments: 0

Show that : Σ_(n=1) ^∞ (((−1)^( n) H_( n) )/n^( 2) ) = −(5/8) ζ (3 ) ■ m.n −−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\mathrm{S}{how}\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\:{n}} \:{H}_{\:{n}} }{{n}^{\:\mathrm{2}} }\:\:=\:−\frac{\mathrm{5}}{\mathrm{8}}\:\zeta\:\left(\mathrm{3}\:\right)\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:−−−−−−−−− \\ $$

Question Number 166435 Answers: 2 Comments: 0

Equation : Solve in R ⌊x⌋ +⌊2x ⌋ +⌊ 3x ⌋=1 −−−−−−−−−

$$ \\ $$$$\:\:\:\:\mathscr{E}{quation}\:: \\ $$$$\:\:\:\:\:{Solve}\:{in}\:\:\mathbb{R}\: \\ $$$$\:\:\:\lfloor{x}\rfloor\:+\lfloor\mathrm{2}{x}\:\rfloor\:+\lfloor\:\mathrm{3}{x}\:\rfloor=\mathrm{1} \\ $$$$\:\:\:\:\:\:−−−−−−−−− \\ $$

Question Number 166431 Answers: 1 Comments: 0

2(2^x /(16,0)) = 5,7^2 − 0,49 + 0 How much the x is?

$$\mathrm{2}\frac{\mathrm{2}^{{x}} }{\mathrm{16},\mathrm{0}}\:=\:\mathrm{5},\mathrm{7}^{\mathrm{2}} \:−\:\mathrm{0},\mathrm{49}\:+\:\mathrm{0} \\ $$$${How}\:{much}\:{the}\:{x}\:{is}? \\ $$

Question Number 166424 Answers: 1 Comments: 3

Question Number 166419 Answers: 1 Comments: 1

Question Number 166417 Answers: 1 Comments: 0

Question Number 166403 Answers: 1 Comments: 1

fog_((3)) =10 f(3)=4 g(x)=?

$${fog}_{\left(\mathrm{3}\right)} =\mathrm{10} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{4} \\ $$$${g}\left({x}\right)=? \\ $$

Question Number 166402 Answers: 1 Comments: 0

f(x)=x^3 +x^2 +13 g(x)=(√5) gof_((x)) =?

$${f}\left({x}\right)={x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{13} \\ $$$${g}\left({x}\right)=\sqrt{\mathrm{5}} \\ $$$${gof}_{\left({x}\right)} =? \\ $$

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