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Find a for which lim(n->oo) (1^a+2^a+3^a...

Find `a` for which `lim_(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+(na+2)+...+(na+n)])=1/60`

A

7

B

8

C

`15/2`

D

`17/2`

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The correct Answer is:
A
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DISHA PUBLICATION-INTEGRALS -EXERCISE-2 CONCEPT APPLICATOR
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  3. Let the equation of a curve passing through the point (0,1) be given b...

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  4. If intf(x)sinxcosx dx=1/(2(b^2-a^2))logf(x)+C, then f(x) is

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  5. If int sqrt2 sqrt (1 + sin x ) dx =- 4 cos (ax +b)+C then the value of...

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  6. Evaluate: int1/(1+3sin^2x+8cos^2x)\ dx

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  7. I = int {log (e) log (e) x + (1)/( (log (e) x ) ^(2))} dx is equal to:

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  8. int(sqrt(x))/(1+4sqrt(x^(3)))dx is equal to

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  9. In the integral int(cos 8x+1)/(cot 2x-tan 2x)dx=A cos 8x+k, where k...

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  10. If |x| lt 1" thn "underset(n to oo)"Lt "(1+x)(1+x^(2))(1+x^(4))....(1+...

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  11. int0^1000 e^(x-[x])dx

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  12. Evaluate: ifintf(x)dx=g(x),t h e nintf^(-1)(x)dx

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  13. int(-pi/4) ^(pi/4) (e^theta(thetasintheta))/(e^(2theta)-1)d theta=

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  14. int (x ^(n-1))/( x ^(2n) + a ^(2)) dx =

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  15. If intf(x)cos x dx = 1/2 f^(2)(x)+C, then f(x) can be

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  16. Evaluate: int2^2^x2^2^xdxdot

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  17. The value of int (sqrt ( log 2 )) ^(sqrt( log 3 )) (x sin x ^(2))/( si...

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  18. The value of int((1+x))/(x(1+x e^(x))^(2))dx, is equal to

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  19. The value of int((ax^2-b)dx)/(xsqrt(c^2x^2-(ax^2+b)^2)) is equal to

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  20. int(log sqrt(pi//2))^(log sqrt(pi))e^(2x)sec^(2)((1)/(3)e^(2x))dx=

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  21. Evaluate : int(6x+7)/(sqrt((x-5)(x-4)))\ dx

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