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Use integral calculus to find the sum of...

Use integral calculus to find the sum of the series `(1)/(4!)+(4l)/(8l)+(8l)/(12l)+……oo.`

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The correct Answer is:
`(1)/(4) ln 2-(pi)/(24).`
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FIITJEE-TIPS-NUERICAL DECIMAL BASED QUATIONS
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  2. If {x} denotes the fractiona part of x, then {(4^(2n))/(15)}, n in N, ...

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  3. Period of sin.(pi)/(4)[x]+sin.(pix)/(2)+tan.(pi)/(3)+sin.(pit)/(4) is

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  4. The period of the function f(t)=sin.(pit)/(3)+sin.(pit)/(4) is

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  5. The value of lim(xrarroo)(x^(3)sin(1//x)-2x^(2))/(1+3x^(2)) is

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  6. Let fp(alpha)=(cos(alpha/p^2)+i sin(alpha/p^2))+((cos)(2alpha)/p^2+isi...

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  7. Evaluate underset(xto0)lim(1-cos(1-cosx))/(x^(4)).

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  8. The value of int(-1)^(1)g(x)-g-(-x)+[x]dx where [.] is the greatest fu...

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  9. Tet alpha, beta and gamma be the roots of f(x) = x^3 + x^2 - 5x - 1 = ...

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  17. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

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  19. intx^6sin(5x^7)dx=k/5cos(5x^7)+c ,then k=

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  20. If int(sqrt(cotx))/(sinx cos x)dx=A sqrt(cotx)+B, then A is equal to

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  21. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h...

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