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Question Number 117365 Answers: 1 Comments: 1
$${Express}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!\:\:{in}\:{terms}\:{of}\:{infinite}\:{series} \\ $$
Question Number 117258 Answers: 1 Comments: 0
$$\frac{\mathrm{4}}{\mathrm{3}}.\frac{\mathrm{9}}{\mathrm{8}}.\frac{\mathrm{49}}{\mathrm{48}}.\frac{\mathrm{121}}{\mathrm{120}}.\frac{\mathrm{169}}{\mathrm{168}}.\frac{\mathrm{289}}{\mathrm{288}}.\frac{\mathrm{529}}{\mathrm{528}}.\frac{\mathrm{831}}{\mathrm{830}}.....\infty \\ $$
Question Number 117207 Answers: 0 Comments: 2
$$\boldsymbol{\mathrm{C}}\mathrm{an}\:\mathrm{anyone}\:\mathrm{recommend}\:\mathrm{a}\:\mathrm{pdf}\:\mathrm{for} \\ $$$$\mathrm{learning}\:\mathrm{hypergeometric}\:\mathrm{functions}? \\ $$
Question Number 117286 Answers: 2 Comments: 0
$${A}\:{person}\:{wants}\:{to}\:{invite}\:{his}\:\mathrm{6}\:{friends}\:{in}\:{a}\:{Dinner}\:{party}. \\ $$$${He}\:{has}\:\mathrm{3}\:{person}\:{to}\:{send}\:{letter}\:{to}\:{them}.{In}\:{how}\:{many}\:{ways} \\ $$$${he}\:{can}\:{invite}\:{his}\:\mathrm{6}\:{friends}? \\ $$
Question Number 117205 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{\boldsymbol{{cos}}^{\mathrm{2}} \mathrm{3}\boldsymbol{{x}}}{\mathrm{1}−\mathrm{2}\boldsymbol{{a}}\centerdot\boldsymbol{{cosx}}+\boldsymbol{{a}}^{\mathrm{2}} }\boldsymbol{{dx}}\:−\:?\:\left(\boldsymbol{{a}}\in\boldsymbol{{C}}/\left\{−\mathrm{1};\:\mathrm{1}\right\}\right) \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{need}}\:\boldsymbol{{a}}\:\boldsymbol{{solution}}\:\boldsymbol{{through}}\:\boldsymbol{{complex}}\:\boldsymbol{{analysis}} \\ $$
Question Number 116965 Answers: 1 Comments: 0
$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} \:\frac{{sin}\left({k}\theta\right)}{{k}\theta} \\ $$
Question Number 116902 Answers: 0 Comments: 0
Question Number 116822 Answers: 3 Comments: 1
$$\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:=? \\ $$
Question Number 116685 Answers: 1 Comments: 0
$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equality}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+...+\left(\mathrm{2p}+\mathrm{1}\right)=\left(\mathrm{p}+\mathrm{1}\right)^{\mathrm{2}\:} \:\:\:\mathrm{p}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{this}\:\mathrm{equality}\:\mathrm{is}\:\mathrm{true}\:\mathrm{when} \\ $$$$\mathrm{we}\:\mathrm{replace}\:\mathrm{p}\:\mathrm{by}\:\mathrm{p}+\mathrm{1} \\ $$
Question Number 116610 Answers: 1 Comments: 1
$$ \\ $$$$\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}{h}} \:+\:\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{{h}} \:=\:\mathrm{1} \\ $$
Question Number 116480 Answers: 1 Comments: 0
$$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+........ \\ $$
Question Number 116443 Answers: 0 Comments: 0
Question Number 116348 Answers: 1 Comments: 2
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\left(\mathrm{5}+\mathrm{x}\right)\left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\:\:\left(\mathrm{x}\neq−\mathrm{1},\mathrm{0}\right) \\ $$
Question Number 115732 Answers: 0 Comments: 1
Question Number 115696 Answers: 0 Comments: 4
$$\mathrm{e}^{\mathrm{x}} =\mathrm{logx} \\ $$
Question Number 115632 Answers: 1 Comments: 6
Question Number 115487 Answers: 0 Comments: 3
Question Number 115298 Answers: 1 Comments: 2
$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{log}\left(\mathrm{y}\right)=\mathrm{0} \\ $$
Question Number 115285 Answers: 0 Comments: 0
$$\:\:\:\:\:\:\:\:...\spadesuit{nice}\:\:\:{topology}\:\spadesuit... \\ $$$${suppose}\:\:\langle{S}\:,\:\tau\:\rangle\:{is}\:\:{Baire}'{s} \\ $$$${space}\:\:\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\cup}}{F}_{{n}} \:\:\:{such} \\ $$$${that}\:\:{F}_{{n}} '{s}\:\:{are}\:{closed}\:{sets}\: \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\exists\:{m}\:;\:{F}_{{m}} ^{\:°} \:\neq\:\varnothing\:\:\:..{m}.{n}.{july} \\ $$$$\:\:\:\:\:\:\:\:\:...\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit... \\ $$
Question Number 115237 Answers: 2 Comments: 0
Question Number 115117 Answers: 1 Comments: 0
$${What}\:{is}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\:{when}\: \\ $$$$\mathrm{3}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{3}} −{ax}^{\mathrm{2}} −{bx}−\mathrm{12}\:{is}\:{completely} \\ $$$${divisible}\:{by}\:{x}^{\mathrm{2}} −\mathrm{3}\:? \\ $$
Question Number 114682 Answers: 1 Comments: 0
Question Number 114615 Answers: 1 Comments: 0
Question Number 114561 Answers: 1 Comments: 0
Question Number 114433 Answers: 1 Comments: 0
$${find}\:{sum}\:{of}\:{the}\:{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} +...+\left(\mathrm{4}{n}−\mathrm{3}\right)^{\mathrm{2}} −\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} \\ $$
Question Number 114343 Answers: 0 Comments: 4
$$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{we}\:\mathrm{place}\:\mathrm{5}\:\mathrm{identical} \\ $$$$\mathrm{books}\:\mathrm{and}\:\mathrm{another}\:\mathrm{6}\:\mathrm{identical}\:\mathrm{books} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{shelf}? \\ $$
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