Question and Answers Forum

Set TheoryQuestion and Answers: Page 3

Question Number 165512 Answers: 0 Comments: 0

Σ_(n=0) ^∞ ((2n+1)/(e^((2n+1)π) +1))=^? (1/(24)) −−−−−−−−−−−−−−by Mr. Levent

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}}{\boldsymbol{\mathrm{e}}^{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\pi} +\mathrm{1}}\overset{?} {=}\frac{\mathrm{1}}{\mathrm{24}} \\ $$$$−−−−−−−−−−−−−−\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{Mr}}.\:\boldsymbol{\mathrm{Levent}} \\ $$

Question Number 165321 Answers: 2 Comments: 0

Question Number 164628 Answers: 1 Comments: 1

60!=abc…nm000…0 m=? n=?

$$\mathrm{60}!=\underline{\boldsymbol{\mathrm{abc}}\ldots\boldsymbol{\mathrm{nm}}\mathrm{000}\ldots\mathrm{0}} \\ $$$$\boldsymbol{\mathrm{m}}=?\:\:\boldsymbol{\mathrm{n}}=? \\ $$

Question Number 164085 Answers: 0 Comments: 0

Question Number 163939 Answers: 0 Comments: 0

An old unsolved question#1132 let S={1,2,3,4,5}, if A,B,C is such that A∩B∩C=∅ A∩B≠∅ A∩C≠∅ how many ways can be choose A,B and C

$$\mathrm{An}\:\mathrm{old}\:\mathrm{unsolved}\:\mathrm{question}#\mathrm{1132} \\ $$$$\mathrm{let}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\},\:\mathrm{if}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{A}\cap\mathrm{B}\cap\mathrm{C}=\varnothing \\ $$$$\mathrm{A}\cap\mathrm{B}\neq\varnothing \\ $$$$\mathrm{A}\cap\mathrm{C}\neq\varnothing \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{be}\:\mathrm{choose}\:\mathrm{A},\mathrm{B}\:\mathrm{and} \\ $$$$\mathrm{C} \\ $$

Question Number 163735 Answers: 0 Comments: 1

Question Number 163435 Answers: 1 Comments: 0

Question Number 163161 Answers: 1 Comments: 0

Question Number 161623 Answers: 2 Comments: 0

Σ_(n=1) ^∞ (((−1)^(n+1) )/(n(n+2)))=?

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

Question Number 161439 Answers: 0 Comments: 1

Question Number 158522 Answers: 1 Comments: 0

Σ_(n=2) ^∞ (((ζ(n)−n))/2^n )=?

$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(\zeta\left({n}\right)−{n}\right)}{\mathrm{2}^{{n}} }=? \\ $$

Question Number 155277 Answers: 2 Comments: 0

Question Number 154544 Answers: 0 Comments: 0

determinant (((prove that)),((Σ_(n=1) ^∞ ((H_n H_n ^((2)) )/n^3 )+Σ_(n=1) ^∞ ((H_n H_n ^((3)) )/n^2 )=((21)/8)𝛇(6)+𝛇^2 (3)))) by Math.Amin 11.fb.96

$$\begin{array}{|c|c|}{\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}}\\{\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} ^{\left(\mathrm{2}\right)} }{\boldsymbol{\mathrm{n}}^{\mathrm{3}} }+\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} ^{\left(\mathrm{3}\right)} }{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }=\frac{\mathrm{21}}{\mathrm{8}}\boldsymbol{\zeta}\left(\mathrm{6}\right)+\boldsymbol{\zeta}^{\mathrm{2}} \left(\mathrm{3}\right)}\\\hline\end{array} \\ $$$${by}\:{Math}.{Amin}\:\:\mathrm{11}.{fb}.\mathrm{96} \\ $$

Question Number 148397 Answers: 0 Comments: 0

Question Number 144639 Answers: 0 Comments: 0

Question Number 141997 Answers: 2 Comments: 0

find two irrational numbers between 0.333.... and 0.444...

$$\mathrm{find}\:\mathrm{two}\:\mathrm{irrational}\:\mathrm{numbers}\: \\ $$$$\mathrm{between}\:\mathrm{0}.\mathrm{333}....\:\mathrm{and}\:\mathrm{0}.\mathrm{444}... \\ $$$$ \\ $$

Question Number 141574 Answers: 0 Comments: 0

Question Number 137689 Answers: 0 Comments: 0

Question Number 137626 Answers: 0 Comments: 0

Question Number 137625 Answers: 0 Comments: 0

Question Number 137014 Answers: 0 Comments: 2

Question Number 135634 Answers: 1 Comments: 0

Question Number 133949 Answers: 0 Comments: 0

Question Number 133419 Answers: 0 Comments: 0

Prove the set {1,2,3,...,1989} can be expressed as the disjoint union of A_1 ,A_2 ,...,A_(117) such that (i) each A_i contains the same number of elements ,and (ii) the sum of all elements of each A_i is the same for i=1,2,3,...,m

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{1989}\right\} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\mathrm{the}\:\mathrm{disjoint} \\ $$$$\mathrm{union}\:\mathrm{of}\:\mathrm{A}_{\mathrm{1}} ,\mathrm{A}_{\mathrm{2}} ,...,\mathrm{A}_{\mathrm{117}} \:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{each}\:\mathrm{A}_{\mathrm{i}} \:\mathrm{contains}\:\mathrm{the}\:\mathrm{same}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:,\mathrm{and} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{each}\:\mathrm{A}_{\mathrm{i}} \:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{for}\:\mathrm{i}=\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{m} \\ $$

Question Number 131164 Answers: 0 Comments: 0

Question Number 129634 Answers: 1 Comments: 0

sin^ x+cos^ x=1 proof by step by step or by showing all steps b/c it is my assignment

$$\boldsymbol{{sin}}^{ } \boldsymbol{{x}}+\boldsymbol{{cos}}^{ } \boldsymbol{{x}}=\mathrm{1}\:\mathrm{proof}\:\mathrm{by}\:\mathrm{step}\:\mathrm{by}\:\mathrm{step}\:\mathrm{or}\:\mathrm{by}\:\mathrm{showing}\:\mathrm{all}\:\mathrm{steps}\: \\ $$$$\mathrm{b}/\mathrm{c}\:\mathrm{it}\:\mathrm{is}\:\mathrm{my}\:\mathrm{assignment} \\ $$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7

Contact: [email protected]