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Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+...

Evaluate: `(lim)_(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]`

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The given limit is
`L=lim_(ntooo) [1/(na)+1/(na+1)+1/(na+2)+………+1/(na+n(b-a))]`
`=lim_(nto oo) sum_(r=0)^((b-a)n)1/(na+r)`
`=lim_(tooo) 1/n sum_(r=0)^((b-a)n)1/(a+r//n)`
`=int_(0)^((b-a))(dx)/(a+x)=[log(a+x)]_(0)^(b-a)`
`=logb-loga=log(b//a)`
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CENGAGE-DEFINITE INTEGRATION -JEE Advanced Previous Year
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