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For a epsilonR (the set of all real numb...

For `a epsilonR` (the set of all real numbers) `a!=-1, lim_(n to oo) ((1^(a)+2^(a)+………+n^(a)))/((n+1)^(a-1)[(na+1)+(na+2)+………..+(na+n)])=1/60`
Then `a=`

A

5

B

7

C

`(-15)/2`

D

`(-17)/2`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Given limit `=(lim_(n to oo) 1/n sum_(r=1)^(n)(r/n)^(a))/(lim_(n to oo) (1+1/n)^(a-1)lim_(n to oo) 1/n sum_(r=1)^(n)(a+r/n))=(int_(0)^(1)x^(a)dx)/(int_(0)^(1)(a+x)dx)`
`=2/((2a+1)(a+1))=2/120`
`:.a=7` or `-17/2`
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