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If the value of ("lim")(nvecoo)(n^(-3/2)...

If the value of `("lim")_(nvecoo)(n^(-3/2))dotsum_(j=1)^(6n)sqrt(j) ` is equal to `sqrt(N) ` then the value of `N/(8)` is __________

Text Solution

Verified by Experts

The correct Answer is:
96
`I=lim_(n to oo)( (sqrt(1)+sqrt(2)+sqrt(3)+………..+sqrt(6n))/(nsqrt(n)))`
`=lim_(nto oo) 1/n sum_(r=1)^(6n)sqrt(r/n)=int_(0)^(6)sqrt(x)dx=[2/3x^(3//2)]_(0)^(6)=2/3 . 6sqrt(6)=sqrt(96)`
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Knowledge Check

  • The value of Lim_(n to oo) n!/((n+1)!-n!)

    A
    a) 0
    B
    b) 1
    C
    c) -1
    D
    d) 2

  • The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

    A
    `(pi)/(4)`
    B
    `(pi)/(2)`
    C
    `(1)/(3)log_(e)2`
    D
    `(1)/(2)log_(e)2`

  • The value of lim_(n to oo)sum_(r=1)^(n)(1)/(n)e^((r)/(n)) is -

    A
    `1-e`
    B
    `e-1`
    C
    e
    D
    `e+1`

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