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Question Number 46617 Answers: 1 Comments: 1

calculate Σ_(n=1) ^∞ (1/(n(n+1)(n+2)(n+3)(n+4)(n+5)))

$${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)\left({n}+\mathrm{4}\right)\left({n}+\mathrm{5}\right)} \\ $$

Question Number 46612 Answers: 1 Comments: 4

1) calculate I_n = ∫_0 ^∞ x^n e^((1−i)x) dx with n integr natural and i^2 =−1 2) find ∫_0 ^∞ x^(4k+3) xsinx dx .

$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:{x}^{{n}} \:{e}^{\left(\mathrm{1}−{i}\right){x}} {dx}\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{x}^{\mathrm{4}{k}+\mathrm{3}} \:{xsinx}\:{dx}\:. \\ $$

Question Number 46611 Answers: 2 Comments: 1

Question Number 46610 Answers: 0 Comments: 2

let f_n (x)=e^(−nx) −2e^(−2nx) with x from[0,+∞[ 1)calculate ∫_0 ^∞ f_n (x)dx and Σ_(n=0) ^∞ (∫_0 ^∞ f_n (x)dx) 2) find S(x)=Σ_(n=0) ^∞ f_n (x) and ∫_0 ^∞ S(x)dx

$${let}\:{f}_{{n}} \left({x}\right)={e}^{−{nx}} −\mathrm{2}{e}^{−\mathrm{2}{nx}} \:\:{with}\:{x}\:{from}\left[\mathrm{0},+\infty\left[\right.\right. \\ $$$$\left.\mathrm{1}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\:\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left(\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right)\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{S}\left({x}\right){dx} \\ $$

Question Number 46609 Answers: 0 Comments: 1

solve x y^(′′) −e^(−x) y^′ =x sinx

$${solve}\:\:\:\:{x}\:{y}^{''} \:−{e}^{−{x}} {y}^{'} \:\:\:={x}\:{sinx} \\ $$

Question Number 46608 Answers: 0 Comments: 0

let the d.e xy^(′′) +(x^2 −x)y^′ +2y =0 find a solution developpable at integr serie.

$${let}\:{the}\:{d}.{e}\:\:{xy}^{''} \:+\left({x}^{\mathrm{2}} −{x}\right){y}^{'} \:+\mathrm{2}{y}\:=\mathrm{0} \\ $$$${find}\:{a}\:{solution}\:{developpable}\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$

Question Number 46607 Answers: 0 Comments: 1

calculate Σ_((i,j)∈ N^2 ) ((i+j)/3^(i+j) )

$${calculate}\:\sum_{\left({i},{j}\right)\in\:{N}^{\mathrm{2}} } \:\:\:\:\:\frac{{i}+{j}}{\mathrm{3}^{{i}+{j}} } \\ $$

Question Number 46604 Answers: 0 Comments: 1

∫_0 ^(π/2) ((xcos x−sin x)/(x^2 +sin x)) dx = ?

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} +\mathrm{sin}\:{x}}\:{dx}\:=\:? \\ $$

Question Number 46598 Answers: 1 Comments: 1

calculate Σ_(n=0) ^∞ arctan((1/(n^2 +n+1)))

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}\right) \\ $$

Question Number 46594 Answers: 1 Comments: 0

find ∫ ((√(x+(√x)))−(√(x−(√x))))dx

$${find}\:\int\:\left(\sqrt{{x}+\sqrt{{x}}}−\sqrt{{x}−\sqrt{{x}}}\right){dx} \\ $$

Question Number 46592 Answers: 2 Comments: 1

Find a solution to: 7x + 5y + 15z + 12w = 149

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}:\:\:\:\mathrm{7x}\:+\:\mathrm{5y}\:+\:\mathrm{15z}\:+\:\mathrm{12w}\:=\:\mathrm{149} \\ $$

Question Number 46586 Answers: 2 Comments: 0

Solve x ∈ R x + (x/(√(x^2 + 1))) = ((35)/(12))

$${Solve}\:\:{x}\:\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\:\frac{{x}}{\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}}\:\:=\:\:\frac{\mathrm{35}}{\mathrm{12}} \\ $$

Question Number 46576 Answers: 0 Comments: 2

Please any note on how to find the first digit, first two digit and first three digits of any power

$$\mathrm{Please}\:\mathrm{any}\:\mathrm{note}\:\mathrm{on}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{digit},\:\mathrm{first}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{and}\:\mathrm{first}\:\mathrm{three}\:\mathrm{digits} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{power} \\ $$

Question Number 46573 Answers: 1 Comments: 4

Show that sin2x ≡((2tanx)/(1+tan^2 x))

$${Show}\:{that}\: \\ $$$${sin}\mathrm{2}{x}\:\equiv\frac{\mathrm{2}{tanx}}{\mathrm{1}+{tan}^{\mathrm{2}} {x}} \\ $$

Question Number 46570 Answers: 1 Comments: 0

If in triangle ABC ((cosB)/b) =((cosC)/c), show that the triangle is isosceles

$${If}\:{in}\:{triangle}\:{ABC}\:\:\:\frac{{cosB}}{{b}}\:=\frac{{cosC}}{{c}},\:{show}\:{that}\:{the} \\ $$$${triangle}\:{is}\:{isosceles} \\ $$

Question Number 46569 Answers: 1 Comments: 0

show that If a^2 ,b^2 ,c^(2 ) are in A.P the cotA,cotB,cotC are also in A.P

$${show}\:{that}\:\:{If}\:{a}^{\mathrm{2}} ,{b}^{\mathrm{2}} ,{c}^{\mathrm{2}\:} \:{are}\:{in}\:{A}.{P}\:\:{the}\:{cotA},{cotB},{cotC}\:{are} \\ $$$${also}\:{in}\:{A}.{P} \\ $$

Question Number 46568 Answers: 0 Comments: 0

show that if the side of a triangle are in A.P, then the cotangent also in A.P

$${show}\:{that}\:{if}\:{the}\:{side}\:{of}\:{a}\:{triangle}\:{are}\:{in}\:{A}.{P}, \\ $$$${then}\:{the}\:{cotangent}\:{also}\:{in}\:{A}.{P} \\ $$

Question Number 46567 Answers: 0 Comments: 0

Solve: 𝚺_(n = 1) ^∞ (((log n)/n))^2

$$\mathrm{Solve}:\:\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\:\:\left(\frac{\mathrm{log}\:\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}}\right)^{\mathrm{2}} \\ $$

Question Number 46563 Answers: 1 Comments: 0

lim_(x→0) (((a^x +b^x +c^x )/3))^(1/x)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{a}^{{x}} +{b}^{{x}} +{c}^{{x}} }{\mathrm{3}}\right)^{\mathrm{1}/{x}} \\ $$

Question Number 46558 Answers: 1 Comments: 0

calculate the uncertainty in velocity of an electron which is confined in a 10^(−10 ) meter

$${calculate}\:{the}\:{uncertainty}\:{in}\:{velocity}\:{of}\:{an}\:{electron}\:{which}\:{is}\:{confined}\:{in}\:{a}\:\mathrm{10}^{−\mathrm{10}\:} {meter} \\ $$

Question Number 46553 Answers: 1 Comments: 0

Can someone please explain me how to solve a quadratic equation without the common formulas but with the sums and products method please ? Thank

$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to} \\ $$$$\mathrm{solve}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\:\mathrm{without}\:\mathrm{the}\: \\ $$$$\mathrm{common}\:\mathrm{formulas}\:\mathrm{but}\:\mathrm{with}\:\mathrm{the}\:\mathrm{sums}\:\mathrm{and} \\ $$$$\mathrm{products}\:\mathrm{method}\:\mathrm{please}\:? \\ $$$$\mathrm{Thank} \\ $$

Question Number 46552 Answers: 1 Comments: 2

Question Number 46549 Answers: 0 Comments: 3

is there any other maths forum apart from this?

$${is}\:{there}\:{any}\:{other}\:{maths}\:{forum}\:{apart}\:{from}\:{this}? \\ $$

Question Number 46546 Answers: 0 Comments: 7

Question Number 46542 Answers: 0 Comments: 5

pls help Find L(cos^2 t)

$${pls}\:{help}\: \\ $$$$\:\boldsymbol{{Find}}\:\boldsymbol{{L}}\left({cos}^{\mathrm{2}} {t}\right) \\ $$

Question Number 46534 Answers: 1 Comments: 0

using taylors expansion find find the value of a)tan45° 1′ b)sin30° 1′

$$\mathrm{using}\:\mathrm{taylors}\:\mathrm{expansion} \\ $$$$\mathrm{find}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left.\mathrm{a}\right)\mathrm{tan45}°\:\mathrm{1}'\: \\ $$$$\left.\mathrm{b}\right)\mathrm{sin30}°\:\mathrm{1}' \\ $$

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