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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 __________

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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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CENGAGE PUBLICATION-DEFINITE INTEGRATION -NUMERICAL VALUE_TYPE
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