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Question Number 123776 Answers: 0 Comments: 0

Another unanswered question ((log1)/( (√1)))−((log3)/( (√3)))+((log5)/( (√5)))−((log7)/( (√7)))+..=((π/4)−(γ/2)−(1/2)log(2π))((1/( (√1)))−(1/( (√3)))+(1/( (√5)))−.)

$A n o t h e r u n a n s w e r e d q u e s t i o n$ $\frac{l o g 1}{\sqrt{1}} - \frac{l o g 3}{\sqrt{3}} + \frac{l o g 5}{\sqrt{5}} - \frac{l o g 7}{\sqrt{7}} + . . = (\frac{π}{4} - \frac{γ}{2} - \frac{1}{2} l o g (2 π)) (\frac{1}{\sqrt{1}} - \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{5}} - .)$

Question Number 123794 Answers: 0 Comments: 0

...mathematical analysis... suppose (X_1 ,τ_1 ) and (X_2 ,τ_2 ) are two topological spaces. prove f:(X_1 ,τ_1 )→(X_2 ,τ_2 ) is a continuous function if only if for any subset A⊆X_1 : f(cl(A))⊆cl(f(A))

$. . . m a t h e m a t i c a l a n a l y s i s . . .$ $s u p p o s e (X_{1}, τ_{1}) a n d (X_{2}, τ_{2})$ $a r e t w o t o p o l o g i c a l s p a c e s .$ $p r o v e f : (X_{1}, τ_{1}) \to (X_{2}, τ_{2}) i s$ $a c o n t i n u o u s f u n c t i o n i f o n l y$ $i f f o r a n y s u b s e t A \subseteq X_{1} :$ $f (c l (A)) \subseteq c l (f (A))$

Question Number 123694 Answers: 0 Comments: 1

sinh((1/1^2 ))+sinh((1/2^2 ))+sinh((1/3^2 ))+....

$s i n h (\frac{1}{1^{2}}) + s i n h (\frac{1}{2^{2}}) + s i n h (\frac{1}{3^{2}}) + . . . .$

Question Number 123653 Answers: 1 Comments: 0

Question Number 123651 Answers: 1 Comments: 0

Question Number 123650 Answers: 0 Comments: 4

1−(1/4)+(1/8)−(1/(10))+(1/(14))−(1/(16))+...

$1 - \frac{1}{4} + \frac{1}{8} - \frac{1}{10} + \frac{1}{14} - \frac{1}{16} + . . .$

Question Number 123620 Answers: 0 Comments: 0

((coth(π))/1^7 )+((coth(2π))/2^7 )+((coth(3π))/3^7 )+...

$\frac{c o t h (π)}{1^{7}} + \frac{c o t h (2 π)}{2^{7}} + \frac{c o t h (3 π)}{3^{7}} + . . .$

Question Number 123460 Answers: 0 Comments: 1

sinh^(−1) (1)+sinh^(−1) ((1/2^2 ))+sinh^(−1) ((1/3^2 ))+sinh^(−1) ((1/4^2 ))+....

${s i n h}^{- 1} (1) + {s i n h}^{- 1} (\frac{1}{2^{2}}) + {s i n h}^{- 1} (\frac{1}{3^{2}}) + {s i n h}^{- 1} (\frac{1}{4^{2}}) + . . . .$

Question Number 123370 Answers: 0 Comments: 2

((√1)/1)+((√2)/5)+((√3)/(10))+((√4)/(17))+((√5)/(37))+...

$\frac{\sqrt{1}}{1} + \frac{\sqrt{2}}{5} + \frac{\sqrt{3}}{10} + \frac{\sqrt{4}}{17} + \frac{\sqrt{5}}{37} + . . .$

Question Number 123336 Answers: 1 Comments: 0

A mercury based barometer reads 760mmhg at the base of a mountain and 704.0mmhg at the top. Find the height of the mountain if the density of mercury and air are respectively 13600kgm^(−3) and 1.25kgm^(−3) (g=10ms^(−2) )

$A mercury based barometer reads$ $760 mmhg at the base of a mountain and$ $704 . 0 mmhg at the top . Find the height$ $of the mountain if the density of$ $mercury and air are respectively$ ${13600 kgm}^{- 3} and 1 . {25 kgm}^{- 3} (g = {10 ms}^{- 2})$

Question Number 123326 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (1/(n^3 +n^2 +n+1))

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

Question Number 123248 Answers: 2 Comments: 3

Find the value of sin((π/9)) in exact form

$F i n d t h e v a l u e o f s i n (\frac{π}{9}) i n e x a c t f o r m$

Question Number 123179 Answers: 0 Comments: 3

(1^7 /(e^(2π) −1))+(2^7 /(e^(4π) −1))+(3^7 /(e^(6π) −1))+....

$\frac{1^{7}}{e^{2 π} - 1} + \frac{2^{7}}{e^{4 π} - 1} + \frac{3^{7}}{e^{6 π} - 1} + . . . .$

Question Number 123167 Answers: 1 Comments: 1

Σ_(n=1) ^∞ ((√n)/(n^2 +n+1))

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

Question Number 123135 Answers: 0 Comments: 0

∫_0 ^∞ ((ta−bt^3 )/((1+ct^2 )(e^(2πt) −1)))dt

$\int_{0}^{\infty} \frac{t a - {b t}^{3}}{(1 + {c t}^{2}) (e^{2 π t} - 1)} d t$

Question Number 122996 Answers: 0 Comments: 1

Σ_(n=1) ^∞ (n/(n^4 +1))

$\underset{n = 1}{\sum^{\infty}} \frac{n}{n^{4} + 1}$

Question Number 122960 Answers: 0 Comments: 2

(1/(1+(1/(2+(3^2 /(2+(5^2 /(2+(7^2 /(....))))))))))=(π/4)

$\frac{1}{1 + \frac{1}{2 + \frac{3^{2}}{2 + \frac{5^{2}}{2 + \frac{7^{2}}{. . . .}}}}} = \frac{π}{4}$

Question Number 122917 Answers: 0 Comments: 0

Σ_(n=1) ^∞ ((tan^(−1) n)/(n^2 +1))

$\underset{n = 1}{\sum^{\infty}} \frac{{t a n}^{- 1} n}{n^{2} + 1}$

Question Number 122862 Answers: 1 Comments: 0

∫_0 ^∞ (x^7 /((1+x)^(10) ))dx

$\int_{0}^{\infty} \frac{x^{7}}{{(1 + x)}^{10}} d x$

Question Number 122740 Answers: 0 Comments: 3

Prove that tanx=(2/(π−2x))−(2/(π+2x))+(2/(3x−2π))−(2/(3x+2π))+(2/(5x−2π))−(2/(5x+2π))+....

$P r o v e t h a t$ $t a n x = \frac{2}{π - 2 x} - \frac{2}{π + 2 x} + \frac{2}{3 x - 2 π} - \frac{2}{3 x + 2 π} + \frac{2}{5 x - 2 π} - \frac{2}{5 x + 2 π} + . . . .$

Question Number 122668 Answers: 0 Comments: 0

Esta has a directory. it contains n (n<1000) pages where 999991 subscribers are registered and each page contains the same numbers of subscribers. How many pages does this directory has?

$E s t a h a s a$ $d i r e c t o r y . i t c o n t a i n s$ $n (n < 1000) p a g e s w h e r e$ $999991 s u b s c r i b e r s a r e r e g i s t e r e d$ $a n d e a c h p a g e c o n t a i n s t h e$ $s a m e n u m b e r s o f s u b s c r i b e r s .$ $H o w m a n y p a g e s d o e s t h i s$ $d i r e c t o r y h a s ?$

Question Number 122641 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (1/(n^4 +1))

$\underset{n = 1}{\sum^{\infty}} \frac{1}{n^{4} + 1}$

Question Number 122638 Answers: 0 Comments: 1

Question Number 122518 Answers: 1 Comments: 1

1−(1/5)+(1/7)−(1/(11))+(1/(13))−(1/(17))+...

$1 - \frac{1}{5} + \frac{1}{7} - \frac{1}{11} + \frac{1}{13} - \frac{1}{17} + . . .$

Question Number 122514 Answers: 2 Comments: 1

Question Number 122336 Answers: 0 Comments: 0

please prove that sup(−A)=−inf(A)

$p l e a s e p r o v e t h a t s u p (- A) = - i n f (A)$

Pg 47 Pg 48 Pg 49 Pg 50 Pg 51 Pg 52 Pg 53 Pg 54 Pg 55 Pg 56

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