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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

$You can't use 'macro parameter character #' in math mode$ $let S = {1, 2, 3, 4, 5}, if A, B, C is such that$ $A \cap B \cap C = \emptyset$ $A \cap B \neq \emptyset$ $A \cap C \neq \emptyset$ $how many ways can be choose A, B and$ $C$

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Σ_(n=1) ^∞ (((−1)^(n+1) )/(n(n+2)))=?

$\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n + 1}}{n (n + 2)} = ?$

Question Number 161439 Answers: 0 Comments: 1

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Σ_(n=2) ^∞ (((ζ(n)−n))/2^n )=?

$\underset{n = 2}{\sum^{\infty}} \frac{(ζ (n) - n)}{2^{n}} = ?$

Question Number 155277 Answers: 2 Comments: 0

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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

$\begin{array}{cc} prove that \\ \underset{n = 1}{\sum^{\infty}} \frac{H_{n} H_{n}^{(2)}}{n^{3}} + \underset{n = 1}{\sum^{\infty}} \frac{H_{n} H_{n}^{(3)}}{n^{2}} = \frac{21}{8} ζ (6) + ζ^{2} (3) \end{array}$ $b y M a t h . A m i n 11 . f b . 96$

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Question Number 141997 Answers: 2 Comments: 0

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

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

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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

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

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

${s i n}^{} x + {c o s}^{} x = 1 proof by step by step or by showing all steps$ $b / c it is my assignment$

Question Number 128246 Answers: 0 Comments: 0

...nice calculus... suppose that :: m=((4^p −1)/3) , where p is a prime number and p>3. prove that ::: 2^(m−1) ≡^m 1 ...?

$. . . n i c e c a l c u l u s . . .$ $s u p p o s e t h a t :: m = \frac{4^{p} - 1}{3}, w h e r e$ $p i s a p r i m e n u m b e r a n d p > 3 .$ $p r o v e t h a t :::$ $2^{m - 1} \overset{m}{\equiv} 1 . . . ?$

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