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If a,b in R^(+) then find Lim(nrarroo) ...

If `a,b in R^(+)` then find `Lim_(nrarroo) sum_(k=1)^(n) ( n)/((k+an)(k+bn))` is equal to

A

`(1)/(a-b) ln'(b(b+1))/(a(a+1))` if `a ne b`

B

`(1)/(a-b) ln'(a(b+1))/(b(a+1))` if `a ne b`

C

non existent if `a = b`

D

`(1)/(a(1+a))` if `a ne b`

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The correct Answer is:
B, D
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
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  2. Let f : R rarr R be defined as f(x) = int(-1)^(e^(x)) (dt)/(1+t^(2)) +...

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  4. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

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  6. Let I(n) = underset(0)overset(1//2)int(1)/(sqrt(1-x^(n))) dx where n ...

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  7. If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then wh...

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  8. Let f(x) = int(0)^(x)|2t-3|dt, then f is

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  9. Let f(x) = int(0)^(pi)(sinx)^(n) dx, n in N then

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  10. Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R, then

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  11. Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then

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  12. Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...

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  13. Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then

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  14. Let f(a,b) = int(a)^(b)(x^(2)-4x+3)dx, (bgt 0) then

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  15. Let I = int(2)^(oo)((2x)/(x^(2)+1)- (1)/(2x+1)) dx & I is a finite r...

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  16. Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...

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  18. Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...

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  19. A function f(x) satisfying int(0)^(1) f(tx)dt=n f(x), where xgt0, is

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  20. Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,and the X-axis.

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