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Lt(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2...

`Lt_(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2))/((n+3)^(3//2))+(n^(1//2))/((n+6)^(3//2))+.......+(n^(1//2))/({n+3(n-1)}^(3//2))]=`

A

`1/3`

B

`1/5`

C

`1/10`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+(1)...

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  2. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+n))+(1)/(sq...

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  3. Lt(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2))/((n+3)^(3//2))+(n^(1//2))/(...

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  4. If S(n)={(1)/(1+sqrt(n))+(1)/(2+sqrt(2n))+(1)/(3+sqrt(3n))+....+(1)/(n...

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  5. {:(" "Lt),(n rarr oo):} 3/n [1 + sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt(...

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  6. {:(" "Lt),(n rarr oo):} ((n!)/(n^(n)))^(1/n)=

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  7. Evaluate the limit . underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^...

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  8. If f(n)= 1/n {(n+1)(n+2)....2n}^(1//n) then {:(" "Lt),(n rarr oo):} f(...

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  9. {:(" "Lt),(n rarr oo):}(((2n)!)/(n!n^(n)))^(1/n)=

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  10. The solution for x of the equation int(sqrt(2))^(x) (dt)/(|t|sqrt(t^(2...

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  11. int(0)^(1)(dx)/(x+sqrt(x))=

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  12. int(0)^(oo) (45a)/((3+a+a t)^(4))dt=

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  13. For a gt 1, b gt 1, the value of int(0)^(oo) (a^(-x)-b^(-x))dx=

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  14. If int(ln 2)^(x) (e^(x)-1)^(-1)dx= ln (3/2) then x=

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  15. int(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx=

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  16. int(2)^(3) (1)/(x^(2)-x) dx=

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  17. int(0)^(3) (3x + 1)/(x^(2)+9)dx=

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  18. int(0)^(1) (dx)/(x^(2)+2x sin alpha +1)=

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  19. int(0)^(pi//4) (sin^(2) x cos^(2) x)/((sin^(3) x + cos^(3)x)^(2))dx=

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  20. int(1//2)^(1) (1)/(sqrt(x-x^(2)))dx=

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