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Question Number 56602    Answers: 1   Comments: 1

Sum the series: sin^2 (α) + sin^2 (2α) + sin^2 (3α) + ... + sin^2 (nα)

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{sin}^{\mathrm{2}} \left(\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2}\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}\alpha\right)\:+\:...\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{n}\alpha\right) \\ $$

Question Number 56597    Answers: 0   Comments: 3

Question Number 56594    Answers: 1   Comments: 0

Find the nth term of the sequence (a) (1/2), (1/4), (1/8), (7/(62)), ... (b) (1/2), (1/4), (1/8), 0, ...

$$\mathrm{Find}\:\mathrm{the}\:{n}\mathrm{th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence} \\ $$$$\left({a}\right)\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{4}},\:\frac{\mathrm{1}}{\mathrm{8}},\:\frac{\mathrm{7}}{\mathrm{62}},\:... \\ $$$$\left({b}\right)\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{4}},\:\frac{\mathrm{1}}{\mathrm{8}},\:\mathrm{0},\:... \\ $$

Question Number 56585    Answers: 0   Comments: 3

Question Number 56584    Answers: 1   Comments: 0

Question Number 56583    Answers: 0   Comments: 1

let f(x) =((cosx)/(x^2 +1)) 1) calculate f^((n)) (x) then f^((n)) (0) 2)calculste f^((n)) (0) 3) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\frac{{cosx}}{{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{then}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){calculste}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 56580    Answers: 1   Comments: 0

(D^3 −2D^2 +9D−18)y=6cos3x

$$\left(\mathrm{D}^{\mathrm{3}} −\mathrm{2D}^{\mathrm{2}} +\mathrm{9D}−\mathrm{18}\right)\mathrm{y}=\mathrm{6cos3x} \\ $$

Question Number 56578    Answers: 0   Comments: 3

Question Number 56629    Answers: 0   Comments: 2

1) calculate I =∫_(−∞) ^(+∞) (dx/(x^2 −i)) and J =∫_(−∞) ^(+∞) (dx/(x^2 −i)) 2) find the value of ∫_(−∞) ^(+∞) (dx/(x^4 +1))

$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 56575    Answers: 1   Comments: 2

Question Number 56569    Answers: 0   Comments: 0

Question Number 56565    Answers: 0   Comments: 2

It is my kind request to those who post questions ...pls go through the details of answer...and give feed back...pls activate yourselves to pay your attention in the details of answer...do not become self satisfied by getting your desired results.. unfurl your mind and act in such away that we get a tip of iceberg of your satisfation.Tanmay

$${It}\:{is}\:{my}\:{kind}\:{request}\:{to}\:{those}\:{who}\:{post}\:{questions} \\ $$$$...{pls}\:{go}\:{through}\:{the}\:{details}\:{of}\:{answer}...{and}\:{give} \\ $$$${feed}\:{back}...{pls}\:{activate}\:{yourselves}\:{to}\:{pay}\:{your} \\ $$$${attention}\:{in}\:{the}\:{details}\:{of}\:{answer}...{do}\:{not}\:{become} \\ $$$${self}\:{satisfied}\:{by}\:{getting}\:{your}\:{desired}\:{results}.. \\ $$$${unfurl}\:{your}\:{mind}\:{and}\:{act}\:{in}\:{such}\:{away}\:{that} \\ $$$${we}\:{get}\:{a}\:{tip}\:{of}\:{iceberg}\:{of}\:{your}\:{satisfation}.{Tanmay} \\ $$

Question Number 56555    Answers: 0   Comments: 7

Question Number 56553    Answers: 1   Comments: 0

solve for m m^8 =3125

$$\mathrm{solve}\:\mathrm{for}\:{m} \\ $$$${m}^{\mathrm{8}} =\mathrm{3125} \\ $$

Question Number 56525    Answers: 4   Comments: 2

Question Number 56524    Answers: 0   Comments: 2

Question Number 56523    Answers: 0   Comments: 2

∫x(√(3x^3 +2)) dx=?

$$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}}\:{dx}=? \\ $$

Question Number 56534    Answers: 1   Comments: 1

Question Number 56510    Answers: 1   Comments: 2

Question Number 56498    Answers: 1   Comments: 1

It is known that 5π<α<((13π)/2). cosα=−(1/4) calculate sin2α

$${It}\:{is}\:{known}\:{that}\:\mathrm{5}\pi<\alpha<\frac{\mathrm{13}\pi}{\mathrm{2}}.\:\:{cos}\alpha=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${calculate}\:\:{sin}\mathrm{2}\alpha \\ $$$$ \\ $$

Question Number 56540    Answers: 5   Comments: 1

Question Number 56481    Answers: 2   Comments: 1

Question Number 56479    Answers: 1   Comments: 0

Please is there any way to reduce a polynomial of 4th degree and solve. Or probably a polynomial of nth power to smaller power.

$$\mathrm{Please}\:\mathrm{is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{reduce}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\:\mathrm{4th}\:\mathrm{degree} \\ $$$$\mathrm{and}\:\mathrm{solve}.\:\:\mathrm{Or}\:\mathrm{probably}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\:\:\mathrm{nth}\:\mathrm{power}\:\mathrm{to}\:\mathrm{smaller} \\ $$$$\mathrm{power}.\: \\ $$

Question Number 56477    Answers: 1   Comments: 0

let x and y be two real numbers if x+y≤10 prove ln(x+1)+ln(y+1)≤2ln6

$$\mathrm{let}\:{x}\:\mathrm{and}\:{y}\:\mathrm{be}\:\mathrm{two}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{if}\:{x}+{y}\leqslant\mathrm{10}\:\mathrm{prove} \\ $$$$\mathrm{ln}\left({x}+\mathrm{1}\right)+\mathrm{ln}\left({y}+\mathrm{1}\right)\leqslant\mathrm{2ln6} \\ $$

Question Number 56471    Answers: 1   Comments: 0

Question Number 56461    Answers: 1   Comments: 0

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