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Question Number 157455    Answers: 1   Comments: 0

Question Number 157454    Answers: 2   Comments: 0

Given 1+(3/y)+(5/y^2 )+(7/y^3 )+(9/y^4 )+...= 71 then 1+(4/y)+(9/y^2 )+((16)/y^3 )+((25)/y^4 )+... =?

$$\:{Given}\:\mathrm{1}+\frac{\mathrm{3}}{{y}}+\frac{\mathrm{5}}{{y}^{\mathrm{2}} }+\frac{\mathrm{7}}{{y}^{\mathrm{3}} }+\frac{\mathrm{9}}{{y}^{\mathrm{4}} }+...=\:\mathrm{71} \\ $$$$\:{then}\:\mathrm{1}+\frac{\mathrm{4}}{{y}}+\frac{\mathrm{9}}{{y}^{\mathrm{2}} }+\frac{\mathrm{16}}{{y}^{\mathrm{3}} }+\frac{\mathrm{25}}{{y}^{\mathrm{4}} }+...\:=? \\ $$

Question Number 157453    Answers: 1   Comments: 0

Question Number 157452    Answers: 0   Comments: 1

solve tan x=cos 3x

$$\:{solve}\:\mathrm{tan}\:{x}=\mathrm{cos}\:\mathrm{3}{x}\: \\ $$

Question Number 157442    Answers: 2   Comments: 0

∫ (dx/(x−(√(x^2 +2x+2))))

$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}}}\: \\ $$

Question Number 157441    Answers: 2   Comments: 0

(7 ((6x−10))^(1/5) )^2 = ((49)/( ((1/x^2 ))^(1/5) ))

$$\:\left(\mathrm{7}\:\sqrt[{\mathrm{5}}]{\mathrm{6x}−\mathrm{10}}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{49}}{\:\sqrt[{\mathrm{5}}]{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}}\: \\ $$

Question Number 157425    Answers: 1   Comments: 0

Question Number 157420    Answers: 2   Comments: 0

∫(1/(u^4 +(1−u)^4 ))du

$$\int\frac{\mathrm{1}}{\boldsymbol{{u}}^{\mathrm{4}} +\left(\mathrm{1}−\boldsymbol{{u}}\right)^{\mathrm{4}} }\boldsymbol{{du}} \\ $$

Question Number 157418    Answers: 0   Comments: 0

Question Number 157417    Answers: 1   Comments: 0

if a;b>0 then prove that: (((a + b)^6 (a^(15) + b^(15) ) (a^(21) + b^(21) ))/((a^3 + b^3 )^2 (a^5 + b^5 )^3 (a^7 + b^7 )^3 )) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b}>\mathrm{0}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{a}\:+\:\mathrm{b}\right)^{\mathrm{6}} \:\left(\mathrm{a}^{\mathrm{15}} \:+\:\mathrm{b}^{\mathrm{15}} \right)\:\left(\mathrm{a}^{\mathrm{21}} \:+\:\mathrm{b}^{\mathrm{21}} \right)}{\left(\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \right)^{\mathrm{2}} \:\left(\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \right)^{\mathrm{3}} \:\left(\mathrm{a}^{\mathrm{7}} \:+\:\mathrm{b}^{\mathrm{7}} \right)^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$$$ \\ $$

Question Number 157416    Answers: 3   Comments: 3

If 2x^2 +11x+5 is a factor of ax^3 −17x^2 +bx−15 , then what is a and b ?

$$\:{If}\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{5}\:{is}\:{a}\:{factor}\:{of} \\ $$$$\:{ax}^{\mathrm{3}} −\mathrm{17}{x}^{\mathrm{2}} +{bx}−\mathrm{15}\:,\:{then}\:{what} \\ $$$${is}\:{a}\:{and}\:{b}\:? \\ $$

Question Number 157412    Answers: 2   Comments: 0

∫_( 0) ^( (π/2)) (x/(sin^8 x+cos^8 x)) dx ?

$$\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{\mathrm{sin}\:^{\mathrm{8}} {x}+\mathrm{cos}\:^{\mathrm{8}} {x}}\:{dx}\:? \\ $$

Question Number 157392    Answers: 1   Comments: 2

Question Number 157389    Answers: 0   Comments: 0

lim_(x→∞) (((6e^x^2 −20ln ∣x∣)/(6e^x^2 −20ln ∣x∣+3)))^(3e^(2x^2 ) sin (((6k)/e^x^2 ))) =26 k=?

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{6}{e}^{{x}^{\mathrm{2}} } −\mathrm{20ln}\:\mid{x}\mid}{\mathrm{6}{e}^{{x}^{\mathrm{2}} } −\mathrm{20ln}\:\mid{x}\mid+\mathrm{3}}\right)^{\mathrm{3}{e}^{\mathrm{2}{x}^{\mathrm{2}} } \:\mathrm{sin}\:\left(\frac{\mathrm{6}{k}}{{e}^{{x}^{\mathrm{2}} } }\right)} =\mathrm{26} \\ $$$$\:{k}=? \\ $$$$ \\ $$

Question Number 157388    Answers: 1   Comments: 2

If m tan (θ − 30°) = n tan (θ + 12°) cos 2θ = ?

$${If}\:\:{m}\:\mathrm{tan}\:\left(\theta\:−\:\mathrm{30}°\right)\:=\:{n}\:\mathrm{tan}\:\left(\theta\:+\:\mathrm{12}°\right) \\ $$$$\mathrm{cos}\:\mathrm{2}\theta\:\:=\:? \\ $$

Question Number 157382    Answers: 1   Comments: 0

Question Number 157379    Answers: 2   Comments: 1

Question Number 157374    Answers: 0   Comments: 3

I see there are idiot comments on this forum. a comment that tells someone not to answer a member's question. this is a provocateur. what's the point of telling people not to answer questions posted by members. If the one who ordered it doesn't want to answer, then do it. no need to tell people to follow you.

$$ \\ $$I see there are idiot comments on this forum. a comment that tells someone not to answer a member's question. this is a provocateur. what's the point of telling people not to answer questions posted by members. If the one who ordered it doesn't want to answer, then do it. no need to tell people to follow you.

Question Number 157351    Answers: 3   Comments: 1

Prove by mathematical induction Σ_(r=1) ^n (1/(r(r+1))) = (n/(n+1))

$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{r}\left({r}+\mathrm{1}\right)}\:=\:\frac{{n}}{{n}+\mathrm{1}} \\ $$

Question Number 157343    Answers: 1   Comments: 0

Question Number 157341    Answers: 0   Comments: 0

Question Number 157332    Answers: 2   Comments: 0

Question Number 157329    Answers: 2   Comments: 0

whats the value of !5

$$\:\boldsymbol{{whats}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\: \\ $$$$\:\:\:\:!\mathrm{5} \\ $$

Question Number 157324    Answers: 1   Comments: 1

Find the general solution for the equation cos 7x − cos 4x + cos x = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{for}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{cos}\:\mathrm{7}{x}\:−\:\mathrm{cos}\:\mathrm{4}{x}\:+\:\mathrm{cos}\:{x}\:=\:\mathrm{0} \\ $$

Question Number 157323    Answers: 2   Comments: 0

Prove that: Ψ_1 ((1/8)) + Ψ_2 ((5/8)) = 32G + 4π^2 Ψ-trigamma function G-catalan constant

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\Psi_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{8}}\right)\:+\:\Psi_{\mathrm{2}} \left(\frac{\mathrm{5}}{\mathrm{8}}\right)\:=\:\mathrm{32G}\:+\:\mathrm{4}\pi^{\mathrm{2}} \\ $$$$\Psi-\mathrm{trigamma}\:\mathrm{function} \\ $$$$\mathrm{G}-\mathrm{catalan}\:\mathrm{constant} \\ $$

Question Number 157315    Answers: 1   Comments: 0

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