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Operation ResearchQuestion and Answers: Page 2

Question Number 140506 Answers: 2 Comments: 0

e^((((ζ(2))/2)−((ζ(3))/3)+((ζ(4))/4)−((ζ(5))/5)+...)) =?

$e^{(\frac{ζ (2)}{2} - \frac{ζ (3)}{3} + \frac{ζ (4)}{4} - \frac{ζ (5)}{5} + . . .)} = ?$

Question Number 140487 Answers: 0 Comments: 0

∫_0 ^∞ ((1/( (√(1+x))))−(1/( (√(1+x^2 )))))(dx/x)=log(2)

$\int_{0}^{\infty} (\frac{1}{\sqrt{1 + x}} - \frac{1}{\sqrt{1 + x^{2}}}) \frac{d x}{x} = l o g (2)$

Question Number 139152 Answers: 0 Comments: 0

wich program to run genetic algorithm?

$w i c h p r o g r a m t o r u n g e n e t i c a l g o r i t h m ?$

Question Number 137575 Answers: 0 Comments: 0

Question Number 137574 Answers: 0 Comments: 0

Question Number 137347 Answers: 1 Comments: 0

(1/(1+(π^2 /(1+(((π+1)^2 )/(1+(((π+2)^2 )/(1+...))))))))+(1/(1+(((π+1)^2 )/(1+(((π+2)^2 )/(1+...))))))=(1/π) Prove or disprove

$\frac{1}{1 + \frac{π^{2}}{1 + \frac{{(π + 1)}^{2}}{1 + \frac{{(π + 2)}^{2}}{1 + . . .}}}} + \frac{1}{1 + \frac{{(π + 1)}^{2}}{1 + \frac{{(π + 2)}^{2}}{1 + . . .}}} = \frac{1}{π}$ $Prove or disprove$

Question Number 137059 Answers: 0 Comments: 0

((1+(1/2^2 )+(1/3^2 )+...)/4^2 )+((1+(1/2^3 )+(1/3^3 )+(1/4^3 )+..)/4^3 )+((1+(1/2^4 )+(1/3^4 )+...)/4^4 )+..=(3/4)log(2)−(π/8)

$\frac{1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . .}{4^{2}} + \frac{1 + \frac{1}{2^{3}} + \frac{1}{3^{3}} + \frac{1}{4^{3}} + . .}{4^{3}} + \frac{1 + \frac{1}{2^{4}} + \frac{1}{3^{4}} + . . .}{4^{4}} + . . = \frac{3}{4} l o g (2) - \frac{π}{8}$

Question Number 136645 Answers: 0 Comments: 0

(1/(1+(η^2 /(1+(((η+1)^2 )/(1+(((η+2)^2 )/(1+(((η+3)^2 )/(1+..)) ))))))))=(1/2)ψ(((η+2)/2))−(1/2)ψ(((η+1)/2)) (η>0) Or K_(r=0) ^∞ (η+r)^2 =(2/(ψ((η/2)+1)−ψ(((η+1)/2))))

$\frac{1}{1 + \frac{η^{2}}{1 + \frac{{(η + 1)}^{2}}{1 + \frac{{(η + 2)}^{2}}{1 + \frac{{(η + 3)}^{2}}{1 + . .}}}}} = \frac{1}{2} ψ (\frac{η + 2}{2}) - \frac{1}{2} ψ (\frac{η + 1}{2}) (η > 0)$ $O r \underset{r = 0}{\overset{\infty}{K}} {(η + r)}^{2} = \frac{2}{ψ (\frac{η}{2} + 1) - ψ (\frac{η + 1}{2})}$

Question Number 135647 Answers: 0 Comments: 0

...+(1/((1−2π^2 )^2 ))+(1/((1−π^2 )^2 ))+1+(1/((1+π^2 )^2 ))+(1/((1+2π^2 )^2 ))+...=((csc^2 ((1/π)))/π^2 )

$. . . + \frac{1}{{(1 - 2 π^{2})}^{2}} + \frac{1}{{(1 - π^{2})}^{2}} + 1 + \frac{1}{{(1 + π^{2})}^{2}} + \frac{1}{{(1 + 2 π^{2})}^{2}} + . . . = \frac{{c s c}^{2} (\frac{1}{π})}{π^{2}}$

Question Number 135127 Answers: 1 Comments: 0

∫_0 ^1 log^2 (Γ(x))dx

$\int_{0}^{1} {l o g}^{2} (Γ (x)) d x$

Question Number 130827 Answers: 1 Comments: 0

[ (x+1)^(2 ) D^2 +(x+1)D+1 ]y = 4cos (ln( x+1))

$[{(x + 1)}^{2} D^{2} + (x + 1) D + 1] y = 4 \cos (\ln (x + 1))$

Question Number 129131 Answers: 0 Comments: 5

Solve 134^(x+1) =16^x −768

$S o l v e 134^{x + 1} = 16^{x} - 768$

Question Number 129102 Answers: 1 Comments: 0

Question Number 124041 Answers: 1 Comments: 1

A_n =(1+(√5))^n −(1−(√5))^n A_n =????

$A_{n} = {(1 + \sqrt{5})}^{n} - {(1 - \sqrt{5})}^{n}$ $A_{n} = ? ? ? ?$

Question Number 123826 Answers: 1 Comments: 1

W_n =Σ_(k=1) ^(2n) (k/(n^2 +k^2 )) montrer que W_n converge et calculer la valeur de W_n

$W_{n} = \underset{k = 1}{\sum^{2 n}} \frac{k}{n^{2} + k^{2}}$ $m o n t r e r q u e W_{n} c o n v e r g e$ $e t c a l c u l e r l a v a l e u r d e W_{n}$

Question Number 119150 Answers: 2 Comments: 0

Given that a, b and c are real numbers that stisfy the system of equation above a − (√(b^2 − (1/(16)) )) = (√(c^2 − (1/(16)) )) b − (√(c^2 − (1/(25)))) = (√(a^2 − (1/(25)) )) c − (√(a^2 − (1/(36)) )) = (√(b^2 − (1/(36)))) if a+ b + c = (x/( (√y))) where x, y are positive integers and y is square free, find the value of x + y !

$G i v e n t h a t a, b a n d c a r e r e a l n u m b e r s$ $t h a t s t i s f y t h e s y s t e m o f e q u a t i o n a b o v e$ $a - \sqrt{b^{2} - \frac{1}{16}} = \sqrt{c^{2} - \frac{1}{16}}$ $b - \sqrt{c^{2} - \frac{1}{25}} = \sqrt{a^{2} - \frac{1}{25}}$ $c - \sqrt{a^{2} - \frac{1}{36}} = \sqrt{b^{2} - \frac{1}{36}}$ $i f a + b + c = \frac{x}{\sqrt{y}} w h e r e x, y a r e p o s i t i v e i n t e g e r s$ $a n d y i s s q u a r e f r e e, f i n d t h e v a l u e o f x + y!$

Question Number 113901 Answers: 0 Comments: 4

when do I use ∣x∣ for (√x^2 )?

$w h e n d o I u s e ∣ x ∣$ $f o r \sqrt{x^{2}} ?$

Question Number 112813 Answers: 0 Comments: 2

A binary operation has the property a∗(b∗c) = (a∗b)•c and that a∗a=1 for all non−zero real numbers a,b and c. (′•′ here represent multiplication). The solution of the equation 2016∗(6∗x)=100 can be written as (p/q) where p and q are relatively prime positive integers. What is q−p?

$A binary operation has the property$ $a * (b * c) = (a * b) ∙ c and that a * a = 1 for$ $all non - zero real numbers a, b and c .$ $(^{'} ∙^{'} here represent multiplication) .$ $The solution of the equation$ $2016 * (6 * x) = 100 can be written as \frac{p}{q}$ $where p and q are relatively prime$ $positive integers . What is q - p ?$