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Question Number 103239 Answers: 1 Comments: 0

Question Number 103236 Answers: 0 Comments: 3

e^e^(e.....∞) =?

$${e}^{{e}^{{e}.....\infty} } =? \\ $$

Question Number 103228 Answers: 1 Comments: 1

Question Number 103223 Answers: 0 Comments: 0

In a card game for four players, a pack of fifty-two cards is dealt round so that each player receives thirteen cards. A hand that contains no card greater than nine is called a yarborough. How many deals are necessary for the probability of at least one hand being a yarborough to be greater than (1/2) ? (Ace ranks high)

$$\:\:\:\:\:\:\:\:\:\mathrm{In}\:\mathrm{a}\:\mathrm{card}\:\mathrm{game}\:\mathrm{for}\:\mathrm{four}\:\mathrm{players},\:\mathrm{a}\:\mathrm{pack}\:\mathrm{of}\:\mathrm{fifty}-\mathrm{two}\:\mathrm{cards}\:\mathrm{is}\:\mathrm{dealt}\:\mathrm{round}\:\mathrm{so} \\ $$$$\:\:\:\:\:\:\mathrm{that}\:\mathrm{each}\:\mathrm{player}\:\mathrm{receives}\:\mathrm{thirteen}\:\mathrm{cards}.\:\mathrm{A}\:\mathrm{hand}\:\mathrm{that}\:\mathrm{contains}\:\mathrm{no}\:\mathrm{card}\:\mathrm{greater}\:\mathrm{than}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{nine}\:\mathrm{is}\:\mathrm{called}\:\mathrm{a}\:\mathrm{yarborough}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{deals}\:\mathrm{are}\:\mathrm{necessary}\:\mathrm{for}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\:\:\:\:\:\:\mathrm{of}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{hand}\:\mathrm{being}\:\mathrm{a}\:\mathrm{yarborough}\:\mathrm{to}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than}\:\frac{\mathrm{1}}{\mathrm{2}}\:?\:\left(\mathrm{Ace}\:\mathrm{ranks}\:\mathrm{high}\right)\:\:\:\:\:\: \\ $$

Question Number 103220 Answers: 1 Comments: 0

∫_0 ^∞ (x^3 /(e^x +1))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{{x}} +\mathrm{1}}{dx} \\ $$

Question Number 103219 Answers: 1 Comments: 3

1+1+1+1+1+1+1+....=S_n S_n =1+1+1+1+1+1+1+.... 2S_n = 2 + 2 + 2+....... .......... subtracting −S_n =1−1+1−1+1−1+1−1+1−1+.... −S_n =(1/2) S_n =−(1/2) I have found this while experiment . I know the sum diverges but is it pretty cool? Kindly rectify me if there is any fault on this non rigorous process I have found some Ramanujan proof S_n =1+2+3+4+5+6+7+... 4S_n = 4+ 8 + 12+... −3S_n =1−2+3−4+5−6+7−8+...... −3S_n =(1/4) S_n =−(1/(12)) Ramanujan had done this on his notebook

$$\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+....={S}_{{n}} \\ $$$${S}_{{n}} =\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+.... \\ $$$$\mathrm{2}{S}_{{n}} =\:\:\:\:\mathrm{2}\:+\:\:\:\:\:\:\mathrm{2}\:\:\:+\:\:\:\:\:\mathrm{2}+....... \\ $$$$..........\:{subtracting} \\ $$$$−{S}_{{n}} =\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+.... \\ $$$$−{S}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:{S}_{{n}} =−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$$${I}\:{have}\:{found}\:{this}\:{while}\:{experiment}\:.\:{I}\:{know}\:{the}\:{sum}\:{diverges} \\ $$$${but}\:{is}\:{it}\:{pretty}\:{cool}?\: \\ $$$${Kindly}\:{rectify}\:{me}\:{if}\:{there}\:{is}\:{any}\:{fault}\:{on}\:{this}\:{non}\:{rigorous} \\ $$$${process} \\ $$$${I}\:{have}\:{found}\:{some}\:{Ramanujan}\:{proof} \\ $$$${S}_{{n}} =\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+... \\ $$$$\mathrm{4}{S}_{{n}} =\:\:\:\:\:\mathrm{4}+\:\:\:\mathrm{8}\:\:\:+\:\mathrm{12}+...\:\:\:\:\: \\ $$$$−\mathrm{3}{S}_{{n}} =\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+\mathrm{5}−\mathrm{6}+\mathrm{7}−\mathrm{8}+...... \\ $$$$−\mathrm{3}{S}_{{n}} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${S}_{{n}} =−\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$ \\ $$$${Ramanujan}\:{had}\:{done}\:{this}\:{on}\:{his}\:{notebook} \\ $$

Question Number 103209 Answers: 3 Comments: 0

Question Number 103205 Answers: 2 Comments: 0

Question Number 103203 Answers: 2 Comments: 0

y′′+4y′+4y = (e^(−2x) /x^2 )

$${y}''+\mathrm{4}{y}'+\mathrm{4}{y}\:=\:\frac{{e}^{−\mathrm{2}{x}} }{{x}^{\mathrm{2}} }\: \\ $$

Question Number 103201 Answers: 2 Comments: 1

(D^2 −2D+1)y = x ln(x)

$$\left({D}^{\mathrm{2}} −\mathrm{2}{D}+\mathrm{1}\right){y}\:=\:{x}\:\mathrm{ln}\left({x}\right) \\ $$

Question Number 103198 Answers: 4 Comments: 1

∫_0 ^1 sin(logx)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {sin}\left({logx}\right){dx} \\ $$

Question Number 103196 Answers: 1 Comments: 0

∫_0 ^1 ((((1/2)−x) ln(1−x) dx)/(x^2 −x+1)) ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}−{x}\right)\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:? \\ $$

Question Number 103195 Answers: 0 Comments: 1

893x = 266 (mod 2432)

$$\mathrm{893}{x}\:=\:\mathrm{266}\:\left({mod}\:\mathrm{2432}\right) \\ $$

Question Number 103193 Answers: 0 Comments: 1

(dy/dx) + y.cot (x) = sin (x)

$$\frac{{dy}}{{dx}}\:+\:{y}.\mathrm{cot}\:\left({x}\right)\:=\:\mathrm{sin}\:\left({x}\right) \\ $$

Question Number 103190 Answers: 1 Comments: 0

∫_(π/4) ^(π/2) ln(ln(tan x)) dx

$$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tan}\:{x}\right)\right)\:{dx}\: \\ $$

Question Number 103186 Answers: 0 Comments: 0

Discuss whether the mean value theorem applies to the function f(x)=(√(x^2 −4)) ?

$${Discuss}\:{whether}\:{the}\:{mean}\:{value}\:{theorem}\: \\ $$$${applies}\:{to}\:{the}\:{function}\:{f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\:? \\ $$

Question Number 103180 Answers: 0 Comments: 0

Let S be a nonempty subset of R that is bounded below . prove that (inf(S)=−sup{−s:s∈S})?

$${Let}\:{S}\:{be}\:{a}\:{nonempty}\:{subset}\:{of}\:{R}\:{that}\:{is}\:{bounded} \\ $$$${below}\:.\:{prove}\:{that}\:\left({inf}\left({S}\right)=−{sup}\left\{−{s}:{s}\in{S}\right\}\right)? \\ $$

Question Number 103179 Answers: 1 Comments: 1

Question Number 103177 Answers: 1 Comments: 0

Find the gineral form of the sequence ⟨2,−2,2,−2,.....⟩?

$${Find}\:{the}\:{gineral}\:{form}\:{of}\:{the}\:{sequence}\:\langle\mathrm{2},−\mathrm{2},\mathrm{2},−\mathrm{2},.....\rangle? \\ $$

Question Number 103171 Answers: 1 Comments: 1

Question Number 103170 Answers: 0 Comments: 3

x^x^x =3 x=?

$${x}^{{x}^{{x}} } =\mathrm{3}\:\:\:\:\:\:{x}=? \\ $$$$ \\ $$

Question Number 103168 Answers: 1 Comments: 0

The particular solution of differential equation of (dy/dx)+(y/x)=k is y=(1/x)+2x thus ,whats the value of k ?

$${The}\:{particular}\:{solution}\:{of}\:{differential}\:{equation}\: \\ $$$${of}\:\frac{{dy}}{{dx}}+\frac{{y}}{{x}}={k}\:{is}\:{y}=\frac{\mathrm{1}}{{x}}+\mathrm{2}{x}\:{thus}\:,{whats}\:{the}\:{value}\:{of}\:{k}\:? \\ $$

Question Number 103165 Answers: 0 Comments: 3

Question Number 103159 Answers: 0 Comments: 1

how do you represent the distance between M andN is 7

$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{represent}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{distance}}\:\boldsymbol{\mathrm{between}} \\ $$$$\boldsymbol{\mathrm{M}}\:{and}\boldsymbol{{N}}\:\mathrm{is}\:\mathrm{7} \\ $$

Question Number 103155 Answers: 0 Comments: 2

If cos^(−1) x+cos^(−1) y+cos^(−1) z+cos^(−1) u=2π, then x^(1999) +y^(2000) +z^(2001) +u^(2002) =

$$\mathrm{If}\:\mathrm{cos}^{−\mathrm{1}} {x}+\mathrm{cos}^{−\mathrm{1}} {y}+\mathrm{cos}^{−\mathrm{1}} {z}+\mathrm{cos}^{−\mathrm{1}} {u}=\mathrm{2}\pi, \\ $$$$\mathrm{then}\:\:{x}^{\mathrm{1999}} +{y}^{\mathrm{2000}} +{z}^{\mathrm{2001}} +{u}^{\mathrm{2002}} = \\ $$

Question Number 103154 Answers: 2 Comments: 0

∫_0 ^1 logxlog(1−x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {logxlog}\left(\mathrm{1}−{x}\right){dx} \\ $$

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