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Question Number 127293 Answers: 0 Comments: 0

Σ_(n=1) ^∞ ((coth(n))/n^3 )

$\underset{n = 1}{\sum^{\infty}} \frac{c o t h (n)}{n^{3}}$

Question Number 127187 Answers: 0 Comments: 1

1−5((1/2))^3 +9((1/2).(3/4))^3 −13((1/2).(3/4).(5/6))^3 +..=(2/π) (prove)

$1 - 5 {(\frac{1}{2})}^{3} + 9 {(\frac{1}{2} . \frac{3}{4})}^{3} - 13 {(\frac{1}{2} . \frac{3}{4} . \frac{5}{6})}^{3} + . . = \frac{2}{π} (p r o v e)$

Question Number 127186 Answers: 0 Comments: 1

∫_0 ^a e^(−x^2 ) dx=((√π)/2)−(e^(−a^2 ) /(2a+(1/(a+(2/(2a+(3/(a+(4/(2a+...)))))))))) (Prove)

$\int_{0}^{a} e^{- x^{2}} d x = \frac{\sqrt{π}}{2} - \frac{e^{- a^{2}}}{2 a + \frac{1}{a + \frac{2}{2 a + \frac{3}{a + \frac{4}{2 a + . . .}}}}} (P r o v e)$

Question Number 127080 Answers: 0 Comments: 1

Σ_(n=1) ^∞ (1/(e^(−φn) +((e^(2πn) −e^(−2φn) )/(2e^(−φn) +((e^(2πn) −e^(−2φn) )/(2e^(−φn) +((e^(2πn) −e^(−2φn) )/(2e^(−2φn) ...))))))))

$\underset{n = 1}{\sum^{\infty}} \frac{1}{e^{- ϕ n} + \frac{e^{2 π n} - e^{- 2 ϕ n}}{2 e^{- ϕ n} + \frac{e^{2 π n} - e^{- 2 ϕ n}}{2 e^{- ϕ n} + \frac{e^{2 π n} - e^{- 2 ϕ n}}{2 e^{- 2 ϕ n} . . .}}}}$

Question Number 127004 Answers: 0 Comments: 1

Question Number 126977 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (n^7 /7^n )

$\underset{n = 1}{\sum^{\infty}} \frac{n^{7}}{7^{n}}$

Question Number 126934 Answers: 1 Comments: 3

(1/(1!))+((1!^2 )/(3!))+((2!^2 )/(5!))+((3!^2 )/(7!))+((4!^2 )/(9!))+....

$\frac{1}{1!} + \frac{1!^{2}}{3!} + \frac{2!^{2}}{5!} + \frac{3!^{2}}{7!} + \frac{4!^{2}}{9!} + . . . .$

Question Number 126913 Answers: 1 Comments: 1

to Tinku tara equation editor is not available in playstore now...pls check..i suggested a few students to dowmload it

$t o T i n k u t a r a$ $e q u a t i o n e d i t o r i s n o t a v a i l a b l e i n p l a y s t o r e$ $n o w . . . p l s c h e c k . . i s u g g e s t e d a f e w s t u d e n t s$ $t o d o w m l o a d i t$

Question Number 126907 Answers: 1 Comments: 0

Merry christmas !! 🎅🤶☃️🌄🎄🦌 🔔🔔🔔🔔🔔🔔🔔🔔🔔 🎄🎄🎄🎄🎄🎄🎄🎄 ∫_0 ^(1/2) ((tanh^(−1) x)/( (x)^(1/5) ))dx

$M e r r y c h r i s t m a s!!$ 🎅🤶☃️🌄🎄🦌 🔔🔔🔔🔔🔔🔔🔔🔔🔔 🎄🎄🎄🎄🎄🎄🎄🎄 $\int_{0}^{\frac{1}{2}} \frac{{t a n h}^{- 1} x}{\sqrt[5]{x}} d x$

Question Number 126780 Answers: 1 Comments: 1

Question Number 126704 Answers: 0 Comments: 0

((e^π −1)/(e^π +1))=(π/(2+(π^2 /(6+(π^2 /(10+(π^2 /(14+....))))))))

$\frac{e^{π} - 1}{e^{π} + 1} = \frac{π}{2 + \frac{π^{2}}{6 + \frac{π^{2}}{10 + \frac{π^{2}}{14 + . . . .}}}}$

Question Number 192126 Answers: 2 Comments: 1

prove that ∣z∣ > ((∣Re(z)∣ +∣Im(z)∣)/2) , ∀z∈C

$p r o v e t h a t$ $∣ z ∣ > \frac{∣ R e (z) ∣ + ∣ I m (z) ∣}{2}, \forall z \in C$

Question Number 126669 Answers: 1 Comments: 2

Σ_(n=1) ^∞ (H_n ^2 /n^4 )

$\underset{n = 1}{\sum^{\infty}} \frac{H_{n}^{2}}{n^{4}}$

Question Number 126632 Answers: 2 Comments: 1

Question Number 126400 Answers: 1 Comments: 5

If a_n =6^n +8^n find (a_(1991) /(49)).

$I f a_{n} = 6^{n} + 8^{n} f i n d \frac{a_{1991}}{49} .$

Question Number 126200 Answers: 0 Comments: 3

(1/1^2 )−(1/2^3 )+(1/3^5 )−(1/4^7 )+(1/5^(11) )−(1/6^(13) )+....

$\frac{1}{1^{2}} - \frac{1}{2^{3}} + \frac{1}{3^{5}} - \frac{1}{4^{7}} + \frac{1}{5^{11}} - \frac{1}{6^{13}} + . . . .$

Question Number 126092 Answers: 2 Comments: 0

A particle starts from rest at time t = 0 and moves in a straightline with variable acceleration a m/s^2 where a = (t/5) , 0 ≤ t ≤ 5 , a = (t/5) + ((10)/t^2 ) , t ≥ 5, t being measured in seconds. Show that the velocity is 22(1/2) m/s when t = 5 and 11 m/s when t = 10. Show also that the distance travelled by the particle in the first 10 seconds is (43(1/3)−10 ln 2) m.

$A particle starts from rest at time t = 0 and moves in$ $a straightline with variable acceleration a m / s^{2} where$ $a = \frac{t}{5}, 0 ⩽ t ⩽ 5, a = \frac{t}{5} + \frac{10}{t^{2}}, t ⩾ 5, t being measured in seconds .$ $Show that the velocity is 22 \frac{1}{2} m / s when t = 5 and$ $11 m / s when t = 10 .$ $Show also that the distance travelled by the particle$ $in the first 10 seconds is (43 \frac{1}{3} - 10 \ln 2) m .$

Question Number 125994 Answers: 1 Comments: 0

((Σ_(n=0) ^∞ e^(−n^2 ) )/(Σ_(n=0) ^∞ e^(−2n^2 ) ))

$\frac{\underset{n = 0}{\sum^{\infty}} e^{- n^{2}}}{\underset{n = 0}{\sum^{\infty}} e^{- 2 n^{2}}}$

Question Number 127492 Answers: 0 Comments: 0

((i!)/(π!)) (Exact form)

$\frac{i!}{π!} (E x a c t f o r m)$

Question Number 125939 Answers: 0 Comments: 0

∫_0 ^1 ((cos2x−tanx.cot(tanx))/(sin2x−tan(tanx)log(cos^2 x)))dx

$\int_{0}^{1} \frac{c o s 2 x - t a n x . c o t (t a n x)}{s i n 2 x - t a n (t a n x) l o g ({c o s}^{2} x)} d x$

Question Number 125884 Answers: 0 Comments: 0

Σ_(n=0) ^∞ ((((√5)−2)^n (((2n)),(n) ))/(((2n+1)(((√5)+(1/( (√5))))^(n+(1/2)) +((√5)−(1/( (√5))))^(n−(1/2)) ))))

$\underset{n = 0}{\sum^{\infty}} \frac{{(\sqrt{5} - 2)}^{n} (\begin{matrix} 2 n \\ n \end{matrix})}{((2 n + 1) ({(\sqrt{5} + \frac{1}{\sqrt{5}})}^{n + \frac{1}{2}} + {(\sqrt{5} - \frac{1}{\sqrt{5}})}^{n - \frac{1}{2}}))}$

Question Number 125857 Answers: 1 Comments: 0

1+4((1/2))^7 +7(((1.3)/(2.4)))^7 +10(((1.3.5)/(2.4.6)))^7 +...

$1 + 4 {(\frac{1}{2})}^{7} + 7 {(\frac{1.3}{2.4})}^{7} + 10 {(\frac{1.3.5}{2.4.6})}^{7} + . . .$

Question Number 125781 Answers: 0 Comments: 0

∫_0 ^∞ ((√x)/(1−x^2 )).(1/(e^(2πx) −1))dx

$\int_{0}^{\infty} \frac{\sqrt{x}}{1 - x^{2}} . \frac{1}{e^{2 π x} - 1} d x$

Question Number 125708 Answers: 1 Comments: 0

∫_0 ^∞ ((1−tanhx)/( ((tanhx))^(1/5) ))dx

$\int_{0}^{\infty} \frac{1 - t a n h x}{\sqrt[5]{t a n h x}} d x$

Question Number 125652 Answers: 0 Comments: 0

Question Number 125585 Answers: 0 Comments: 5

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

$\frac{{(\frac{1}{1!})}^{2} - {(\frac{1}{2!})}^{2} + {(\frac{1}{3!})}^{2} - {(\frac{1}{4!})}^{2} + . . .}{{(\frac{1}{1!})}^{2} + {(\frac{1}{2!})}^{2} + {(\frac{1}{3!})}^{2} + . . . . . .}$

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