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underset(n to oo)lim (1+3+6+...+n(n+1)//...

`underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=`

A

`(1)/(6)`

B

`(1)/(12)`

C

`(1)/(18)`

D

`(1)/(24)`

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Verified by Experts

The correct Answer is:
A
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AAKASH SERIES-LIMITS-EXERCISE-II
  1. underset(n to oo)lim (1+3+3^(2)+...3^(n))/(1+2+2^(2)+...+2^(n))=

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  2. Lt(x to oo) (1+(1)/(3)+(1)/(9)+.....+(1)/(3^(n)))/(1+(1)/(5)+(1)/(25)+...

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  3. underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=

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  4. Lt(x to oo)[(1)/(n^(2)-1)+(2)/(n^(2)-1)+....+(n)/(n^(2)-1)]=

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  5. If 0lt x lt y then Lt(x to oo) (y^(n)+x^(n))^(1//n)=

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  6. Lt(x to oo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

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  7. If 0 lt a< b then Lt(x to oo) (a^(n+3)+b^(n+3))/(a^(n)+b^(n))=

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  8. underset(n to oo)lim (1.1!+2.2!+3.3!+...+n.n!)/((n+1)!)=

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  9. Lt(x to oo) ((1)/(a(a+d))+(1)/((a+d)(a+2d))+.....+(1)/([a+(n-1)d][a+n...

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  10. Lt(n to oo) ((1)/(1.5)+(1)/(5.9)+....+(1)/((4n-3)(4n+1)))=

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  11. f(x)={(x)/(1+x)+(x)/((1+x)(1+2x))+(x)/((1+2x)(1+3x))+....n terms} and ...

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

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  13. If [.] denote the greatest ineger function then Lt(x to oo) ([x]+[2x]+...

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  14. If [.] denotes the greatest integer functon, then Lt(n to oo)([1^(3)x]...

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  15. Let f: R to R be a positive increasing function with Lt(x to oo)(f(3x)...

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  16. underset(x to 1)lim (1-x) tan(pix//2)=

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  17. Determine Lt(x to 0)((1)/(sin^(2))x-(1)/(sin h^(2)x))(oo-oo "from")

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  18. Lt(x to oo) {sqrt(x^(2)-sqrt(x^(4)+1))-x sqrt(2)}=

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  19. underset(x to oo)"Lt"sqrt [({x-sin x})/(x+cos^(2)(x))]=

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  20. underset(x to oo)lim {sin sqrt(x+1)-sin sqrtx)=

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