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Question Number 30123 Answers: 0 Comments: 3

find the convergence or divergence Σ_(n = 1) ^∞ (((n − 1)/n))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{or}\:\mathrm{divergence}\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right) \\ $$

Question Number 30120 Answers: 2 Comments: 1

Question Number 30119 Answers: 2 Comments: 1

Let N= 2^(1224) −1. S= 2^(153) +2^(77) +1. T= 2^(408) −2^(204) +1. then which of the following statment is correct? a) S and T both divide N. b) only S divides N. c) only T divides N. d) Neither S nor T divides N.

$$\mathrm{Let}\:\:\mathrm{N}=\:\mathrm{2}^{\mathrm{1224}} \:−\mathrm{1}. \\ $$$$\mathrm{S}=\:\mathrm{2}^{\mathrm{153}} +\mathrm{2}^{\mathrm{77}} +\mathrm{1}. \\ $$$$\mathrm{T}=\:\mathrm{2}^{\mathrm{408}} −\mathrm{2}^{\mathrm{204}} +\mathrm{1}. \\ $$$$\mathrm{then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statment}\:\mathrm{is} \\ $$$$\:\mathrm{correct}? \\ $$$$\left.\mathrm{a}\right)\:\mathrm{S}\:\mathrm{and}\:\mathrm{T}\:\mathrm{both}\:\mathrm{divide}\:\mathrm{N}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{only}\:\mathrm{S}\:\mathrm{divides}\:\mathrm{N}. \\ $$$$\left.\mathrm{c}\right)\:\mathrm{only}\:\mathrm{T}\:\mathrm{divides}\:\mathrm{N}. \\ $$$$\left.\mathrm{d}\right)\:\mathrm{Neither}\:\mathrm{S}\:\mathrm{nor}\:\mathrm{T}\:\mathrm{divides}\:\mathrm{N}. \\ $$

Question Number 30106 Answers: 1 Comments: 0

Question Number 30094 Answers: 0 Comments: 5

Question Number 30092 Answers: 1 Comments: 0

If x+(1/x)=3 find x^5 +(1/x^5 )

$${If}\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:{find}\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} } \\ $$

Question Number 30173 Answers: 0 Comments: 1

let u_n = Π_(k=1) ^n (1+(k/n^2 )) 1. verify that x−(x^2 /2) ≤ln(1+x)≤x 2. prove that (u_n ) is convergente and find its limit.

$${let}\:{u}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{n}} \:\left(\mathrm{1}+\frac{{k}}{{n}^{\mathrm{2}} }\right) \\ $$$$\mathrm{1}.\:{verify}\:{that}\:{x}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:\leqslant{ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\mathrm{2}.\:{prove}\:{that}\:\left({u}_{{n}} \right)\:{is}\:{convergente}\:{and}\:{find}\:{its}\:{limit}. \\ $$

Question Number 30090 Answers: 1 Comments: 0

if ΔABC similar ΔPQR and area of ΔPQR=4area(ΔABC) then AB:PQ is

$$\mathrm{if}\:\Delta\mathrm{ABC}\:\mathrm{similar}\:\Delta\mathrm{PQR}\:\mathrm{and}\:\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{PQR}=\mathrm{4area}\left(\Delta\mathrm{ABC}\right)\:\mathrm{then}\:\mathrm{AB}:\mathrm{PQ}\:\mathrm{is} \\ $$

Question Number 30089 Answers: 0 Comments: 0

prove the convergence or divergence of (((n − 1)/n))_(n = 1) ^∞

$$\mathrm{prove}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{or}\:\mathrm{divergence}\:\mathrm{of}\:\:\:\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right)_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \\ $$

Question Number 30087 Answers: 3 Comments: 0

solve: cos3x.cos^3 x+sin 3x.sin^3 x=0.

$$\mathrm{solve}: \\ $$$$\mathrm{cos3}{x}.{cos}^{\mathrm{3}} {x}+\mathrm{sin}\:\mathrm{3}{x}.\mathrm{sin}\:^{\mathrm{3}} {x}=\mathrm{0}. \\ $$

Question Number 30079 Answers: 4 Comments: 1

Question Number 30054 Answers: 1 Comments: 0

Question Number 30049 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ ((n(n+1))/3^n ) .

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{3}^{{n}} }\:. \\ $$

Question Number 30045 Answers: 1 Comments: 2

Question Number 30030 Answers: 1 Comments: 2

Question Number 30017 Answers: 1 Comments: 0

find the elements of the ellipse given the following equation 1.(x^2 /(25))+(y^2 /4)=1 2.x^2 +9y^2 =9

$$\mathrm{find}\:\mathrm{the}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}\:\mathrm{given}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation} \\ $$$$\mathrm{1}.\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{25}}+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{1} \\ $$$$\mathrm{2}.\mathrm{x}^{\mathrm{2}} +\mathrm{9y}^{\mathrm{2}} =\mathrm{9} \\ $$

Question Number 30008 Answers: 0 Comments: 1

integrate w.r.t x ∫(e^x^2 )dx

$${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\left({e}^{{x}^{\mathrm{2}} } \right){dx} \\ $$

Question Number 30002 Answers: 0 Comments: 5

Question Number 29998 Answers: 0 Comments: 0

Question Number 29989 Answers: 1 Comments: 0

Question Number 29987 Answers: 0 Comments: 0

prove that Σ_(n=1_(n≠p) ) ^∞ (1/(n^2 −p^2 )) = (3/(4p^2 )) .

$${prove}\:{that}\:\:\sum_{{n}=\mathrm{1}_{{n}\neq{p}} } ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:−{p}^{\mathrm{2}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{4}{p}^{\mathrm{2}} }\:. \\ $$

Question Number 29986 Answers: 1 Comments: 1

find Σ_(n=0) ^∞ ((n+1)/4^n ) .

$${find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{n}+\mathrm{1}}{\mathrm{4}^{{n}} }\:. \\ $$

Question Number 29985 Answers: 0 Comments: 0

prove that Σ_(p=1) ^∞ (a^p /(1−a^(2p) )) = Σ_(p=1) ^∞ (a^(2p−1) /(1−a^(2p−1) )) .

$${prove}\:{that}\:\:\:\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\:\:\:\:\:\frac{{a}^{{p}} }{\mathrm{1}−{a}^{\mathrm{2}{p}} }\:=\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{{a}^{\mathrm{2}{p}−\mathrm{1}} }{\mathrm{1}−{a}^{\mathrm{2}{p}−\mathrm{1}} }\:. \\ $$

Question Number 29984 Answers: 0 Comments: 0

prove that Σ_(n=1) ^∞ (H_n /(n!))==e Σ_(n=1) ^∞ (((1)^(n−1) )/(n (n!))) .

$${prove}\:{that}\:\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{H}_{{n}} }{{n}!}=={e}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} }{\boldsymbol{{n}}\:\left(\boldsymbol{{n}}!\right)}\:. \\ $$

Question Number 29983 Answers: 0 Comments: 1

find radius andsum of Σ_(n=1) ^∞ ((n−1)/(n!)) x^n .

$${find}\:{radius}\:{andsum}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}−\mathrm{1}}{{n}!}\:{x}^{{n}} . \\ $$

Question Number 29982 Answers: 0 Comments: 0

let give f(x)=(√(x+(√(1+x^2 )))) developp f at integr series in point 0

$${let}\:{give}\:{f}\left({x}\right)=\sqrt{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}}\:\:\:\:{developp}\:{f}\:{at}\:{integr}\:{series} \\ $$$${in}\:{point}\:\mathrm{0} \\ $$

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