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Question Number 143225 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (1/((2021^n )(n!))) = Σ_(n=0) ^∞ (1/((2021^n )(∫_0 ^( ∞) t^n .e^(−t) dt)))

$\underset{n = 0}{\sum^{\infty}} \frac{1}{(2021^{n}) (n!)} = \underset{n = 0}{\sum^{\infty}} \frac{1}{(2021^{n}) (\int_{0}^{\infty} t^{n} . e^{- t} d t)}$

Question Number 143072 Answers: 1 Comments: 0

Question Number 142931 Answers: 0 Comments: 0

Question Number 142712 Answers: 0 Comments: 0

Question Number 142553 Answers: 2 Comments: 0

Evaluate : ∫_0 ^1 ((log(x)log((x/(1−x))))/( (√(x/(1−x))))) dx

$E v a l u a t e :$ $\int_{0}^{1} \frac{l o g (x) l o g (\frac{x}{1 - x})}{\sqrt{\frac{x}{1 - x}}} d x$

Question Number 142383 Answers: 1 Comments: 1

Question Number 142359 Answers: 0 Comments: 0

Question Number 142301 Answers: 1 Comments: 0

Question Number 142035 Answers: 1 Comments: 0

(1/2^(1/4) ).(3^(1/9) /4^(1/16) ).(5^(1/25) /6^(1/36) ).(7^(1/49) /8^(1/64) )...=exp(−((ζ′(2))/2)−(π^2 /(12))log (2))

$\frac{1}{2^{1 / 4}} . \frac{3^{1 / 9}}{4^{1 / 16}} . \frac{5^{1 / 25}}{6^{1 / 36}} . \frac{7^{1 / 49}}{8^{1 / 64}} . . . = e x p (- \frac{ζ^{'} (2)}{2} - \frac{π^{2}}{12} \log (2))$

Question Number 141791 Answers: 4 Comments: 0

Calculate Σ_(n=1) ^(+∞) (n^2 /3^n )

$Calculate$ $\underset{n = 1}{\sum^{+ \infty}} \frac{n^{2}}{3^{n}}$

Question Number 141733 Answers: 0 Comments: 0

Question Number 141598 Answers: 1 Comments: 0

Question Number 141611 Answers: 0 Comments: 1

Evaluate: ∫log(ex^2 )^x^(logx)

$E v a l u a t e :$ $\int l o g {({e x}^{2})}^{x^{l o g x}}$

Question Number 141494 Answers: 0 Comments: 0

(((0 −1)),((0 0)) )!= (((1 γ)),((0 1)) ) γ=Euler Mascheroni Constant What is the physical representation of a Matrix factorial?

$(\begin{matrix} 0 - 1 \\ 0 0 \end{matrix})! = (\begin{matrix} 1 γ \\ 0 1 \end{matrix}) γ = E u l e r M a s c h e r o n i C o n s t a n t$ $W h a t i s t h e p h y s i c a l r e p r e s e n t a t i o n o f a M a t r i x f a c t o r i a l ?$

Question Number 141359 Answers: 0 Comments: 2

Question Number 141345 Answers: 0 Comments: 0

((log(ζ(s)))/s)=∫_1 ^∞ J(x)x^(−s−1) dx ( Prove that) Here J(x)=π(x)+(1/2)π((√x))+(1/3)π((x)^(1/3) )+... π(x):=Prime counting function

$\frac{l o g (ζ (s))}{s} = \int_{1}^{\infty} J (x) x^{- s - 1} d x (P r o v e t h a t)$ $H e r e J (x) = π (x) + \frac{1}{2} π (\sqrt{x}) + \frac{1}{3} π (\sqrt[3]{x}) + . . .$ $π (x) := P r i m e c o u n t i n g f u n c t i o n$

Question Number 141313 Answers: 0 Comments: 0

Question Number 141308 Answers: 1 Comments: 0

Question Number 141303 Answers: 3 Comments: 1

Question Number 141304 Answers: 0 Comments: 1

Question Number 141380 Answers: 0 Comments: 0

Question Number 141283 Answers: 0 Comments: 0

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

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

Question Number 141045 Answers: 0 Comments: 4

Question Number 141017 Answers: 2 Comments: 1

Question Number 140916 Answers: 0 Comments: 4

Question Number 140829 Answers: 1 Comments: 0

factorise 5x^(2m) 8x^m +8

$f a c t o r i s e 5 x^{2 m} 8 x^{m} + 8$

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