The value of `lim_(n rarr oo)(1/sqrt(4n^(2)-1)+1/sqrt(4n^(2)-4)+...+1/sqrt(4n^(2)-n^(2)))` is -
The value of `lim_(n rarr oo)(1/sqrt(4n^(2)-1)+1/sqrt(4n^(2)-4)+...+1/sqrt(4n^(2)-n^(2)))` is -
A. `1/4`
B. `pi/12`
C. `pi/4`
D. `pi/6`
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Correct Answer - D
`lim_(n rarr oo) sum_(r=1)^(n) (1)/sqrt(4n^(2)-r^(2))=lim_(n rarr oo)1/n sum_(r=1)^(n) (1)/sqrt(4-(r//n)^(2))`
`=underset(0)overset(1)(int) (dx)/sqrt(4-x^(2))=(sin^(-1) (x/2))_(0)^(1)=pi/6`
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