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Question Number 118323 Answers: 0 Comments: 0

Prove that ζ(1−s)=2^(1−s) π^(−s) cos(((sπ)/2))Γ(s)ζ(s)

$${Prove}\:{that}\: \\ $$$$\zeta\left(\mathrm{1}−{s}\right)=\mathrm{2}^{\mathrm{1}−{s}} \pi^{−{s}} {cos}\left(\frac{{s}\pi}{\mathrm{2}}\right)\Gamma\left({s}\right)\zeta\left({s}\right) \\ $$

Question Number 117990 Answers: 1 Comments: 0

(2.3.5.7.9.11.13.17......∞)×(√(6/(3.8.24.48.80.120.168.288.....∞)))

$$\left(\mathrm{2}.\mathrm{3}.\mathrm{5}.\mathrm{7}.\mathrm{9}.\mathrm{11}.\mathrm{13}.\mathrm{17}......\infty\right)×\sqrt{\frac{\mathrm{6}}{\mathrm{3}.\mathrm{8}.\mathrm{24}.\mathrm{48}.\mathrm{80}.\mathrm{120}.\mathrm{168}.\mathrm{288}.....\infty}} \\ $$

Question Number 117980 Answers: 0 Comments: 2

Where is the quiz?

$$\mathrm{Where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{quiz}? \\ $$$$ \\ $$

Question Number 117645 Answers: 1 Comments: 0

Question Number 117620 Answers: 5 Comments: 0

x^4 −⌊5x^2 ⌋+4=0

$${x}^{\mathrm{4}} −\lfloor\mathrm{5}{x}^{\mathrm{2}} \rfloor+\mathrm{4}=\mathrm{0} \\ $$

Question Number 117475 Answers: 1 Comments: 0

(6/5).((24)/(23)).((54)/(53)).((96)/(95)).((150)/(149)).((216)/(215)).((294)/(293))....

$$\frac{\mathrm{6}}{\mathrm{5}}.\frac{\mathrm{24}}{\mathrm{23}}.\frac{\mathrm{54}}{\mathrm{53}}.\frac{\mathrm{96}}{\mathrm{95}}.\frac{\mathrm{150}}{\mathrm{149}}.\frac{\mathrm{216}}{\mathrm{215}}.\frac{\mathrm{294}}{\mathrm{293}}.... \\ $$

Question Number 117460 Answers: 0 Comments: 2

((2(√2))/(9801))Σ_(n=1) ^∞ (((4n)!(1103+26390n))/((n!)^4 396^(4n) ))=(1/π) (Prove that)

$$\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{9801}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{4}{n}\right)!\left(\mathrm{1103}+\mathrm{26390}{n}\right)}{\left({n}!\right)^{\mathrm{4}} \mathrm{396}^{\mathrm{4}{n}} }=\frac{\mathrm{1}}{\pi}\:\:\:\left({Prove}\:{that}\right) \\ $$

Question Number 117458 Answers: 1 Comments: 0

(4/3).((16)/(15)).((36)/(35)).((64)/(63)).((100)/(99)).((144)/(143)).((196)/(195)).((256)/(255)).((324)/(323))......∞

$$\frac{\mathrm{4}}{\mathrm{3}}.\frac{\mathrm{16}}{\mathrm{15}}.\frac{\mathrm{36}}{\mathrm{35}}.\frac{\mathrm{64}}{\mathrm{63}}.\frac{\mathrm{100}}{\mathrm{99}}.\frac{\mathrm{144}}{\mathrm{143}}.\frac{\mathrm{196}}{\mathrm{195}}.\frac{\mathrm{256}}{\mathrm{255}}.\frac{\mathrm{324}}{\mathrm{323}}......\infty \\ $$

Question Number 117391 Answers: 1 Comments: 0

(√(2/3))−(√(2/(27)))+(√(2/(75)))−(√(2/(147)))+(√(2/(243)))−(√(2/(363)))+(√(2/(507)))−(√(2/(675)))+(√(2/(867)))−._ ...

$$\sqrt{\frac{\mathrm{2}}{\mathrm{3}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{27}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{75}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{147}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{243}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{363}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{507}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{675}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{867}}}−._{} ... \\ $$

Question Number 117366 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (((2n)!)/(n^(2n) n!(2n+1)))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2}{n}\right)!}{{n}^{\mathrm{2}{n}} {n}!\left(\mathrm{2}{n}+\mathrm{1}\right)} \\ $$

Question Number 117365 Answers: 1 Comments: 1

Express ((1/2))! in terms of infinite series

$${Express}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!\:\:{in}\:{terms}\:{of}\:{infinite}\:{series} \\ $$

Question Number 117258 Answers: 1 Comments: 0

(4/3).(9/8).((49)/(48)).((121)/(120)).((169)/(168)).((289)/(288)).((529)/(528)).((831)/(830)).....∞

$$\frac{\mathrm{4}}{\mathrm{3}}.\frac{\mathrm{9}}{\mathrm{8}}.\frac{\mathrm{49}}{\mathrm{48}}.\frac{\mathrm{121}}{\mathrm{120}}.\frac{\mathrm{169}}{\mathrm{168}}.\frac{\mathrm{289}}{\mathrm{288}}.\frac{\mathrm{529}}{\mathrm{528}}.\frac{\mathrm{831}}{\mathrm{830}}.....\infty \\ $$

Question Number 117207 Answers: 0 Comments: 2

Can anyone recommend a pdf for learning hypergeometric functions?

$$\boldsymbol{\mathrm{C}}\mathrm{an}\:\mathrm{anyone}\:\mathrm{recommend}\:\mathrm{a}\:\mathrm{pdf}\:\mathrm{for} \\ $$$$\mathrm{learning}\:\mathrm{hypergeometric}\:\mathrm{functions}? \\ $$

Question Number 117286 Answers: 2 Comments: 0

A person wants to invite his 6 friends in a Dinner party. He has 3 person to send letter to them.In how many ways he can invite his 6 friends?

$${A}\:{person}\:{wants}\:{to}\:{invite}\:{his}\:\mathrm{6}\:{friends}\:{in}\:{a}\:{Dinner}\:{party}. \\ $$$${He}\:{has}\:\mathrm{3}\:{person}\:{to}\:{send}\:{letter}\:{to}\:{them}.{In}\:{how}\:{many}\:{ways} \\ $$$${he}\:{can}\:{invite}\:{his}\:\mathrm{6}\:{friends}? \\ $$

Question Number 117205 Answers: 0 Comments: 0

∫_0 ^( 2π) ((cos^2 3x)/(1−2a∙cosx+a^2 ))dx − ? (a∈C/{−1; 1}) I need a solution through complex analysis

$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{\boldsymbol{{cos}}^{\mathrm{2}} \mathrm{3}\boldsymbol{{x}}}{\mathrm{1}−\mathrm{2}\boldsymbol{{a}}\centerdot\boldsymbol{{cosx}}+\boldsymbol{{a}}^{\mathrm{2}} }\boldsymbol{{dx}}\:−\:?\:\left(\boldsymbol{{a}}\in\boldsymbol{{C}}/\left\{−\mathrm{1};\:\mathrm{1}\right\}\right) \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{need}}\:\boldsymbol{{a}}\:\boldsymbol{{solution}}\:\boldsymbol{{through}}\:\boldsymbol{{complex}}\:\boldsymbol{{analysis}} \\ $$

Question Number 116965 Answers: 1 Comments: 0

Σ_(k=1) ^∞ (−1)^(k+1) ((sin(kθ))/(kθ))

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} \:\frac{{sin}\left({k}\theta\right)}{{k}\theta} \\ $$

Question Number 116902 Answers: 0 Comments: 0

Question Number 116822 Answers: 3 Comments: 1

what the value of (√i) =?

$$\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:=? \\ $$

Question Number 116685 Answers: 1 Comments: 0

Given the equality: 1+3+5+...+(2p+1)=(p+1)^(2 ) p ∈ N^∗ Show this equality is true when we replace p by p+1

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equality}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+...+\left(\mathrm{2p}+\mathrm{1}\right)=\left(\mathrm{p}+\mathrm{1}\right)^{\mathrm{2}\:} \:\:\:\mathrm{p}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{this}\:\mathrm{equality}\:\mathrm{is}\:\mathrm{true}\:\mathrm{when} \\ $$$$\mathrm{we}\:\mathrm{replace}\:\mathrm{p}\:\mathrm{by}\:\mathrm{p}+\mathrm{1} \\ $$

Question Number 116610 Answers: 1 Comments: 1

solve : ((1/( (√2))))^(2h) + (((√3)/2))^h = 1

$$ \\ $$$$\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}{h}} \:+\:\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{{h}} \:=\:\mathrm{1} \\ $$

Question Number 116480 Answers: 1 Comments: 0

(1/8)+(1/(18))+(1/(30))+(1/(44))+(1/(60))+(1/(78))+(1/(98))+(1/(120))+........

$$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+........ \\ $$

Question Number 116443 Answers: 0 Comments: 0

Question Number 116348 Answers: 1 Comments: 2

Find the minimum value of (((5+x)(2+x)^2 )/(x(1+x))) (x≠−1,0)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\left(\mathrm{5}+\mathrm{x}\right)\left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\:\:\left(\mathrm{x}\neq−\mathrm{1},\mathrm{0}\right) \\ $$

Question Number 115732 Answers: 0 Comments: 1

Question Number 115696 Answers: 0 Comments: 4

e^x =logx

$$\mathrm{e}^{\mathrm{x}} =\mathrm{logx} \\ $$

Question Number 115632 Answers: 1 Comments: 6

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