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If the value of lim(n to oo) (n^(-3//2))...

If the value of `lim_(n to oo) (n^(-3//2))`. `sum_(j=1)^(6n)sqrt(j)` is equal to `sqrt(N)`, then the value of `N` 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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