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Compute the limit underset(n rarr oo)("l...

Compute the limit `underset(n rarr oo)("lim") ((1)/(sqrt(4n^(2)-1)) + (1)/(sqrt(4n^(2)-2^(2))) +……+ (1)/(sqrt(4n^(2)-n^(2))))`

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/(6)`
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Evaluate: lim_(n rarr oo)((1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-2^(2)))+...+(1)/(sqrt(3n^(2))))

Find underset( n rarr oo) ("lim") (sqrt( n^(2) + 1)+ sqrt( n ) )/( sqrt( n ^(2) + 1)- sqrt( n ) )

Knowledge Check

  • lim_(n rarr oo) [(1)/(sqrt""(n^(2)-1)) + (1)/(sqrt""(n^(2) + 2^(2)))+ ….+ (1)/([n^(2)- (n-1)^(2)])] = ….

    A
    0
    B
    `(pi)/(2)`
    C
    `pi`
    D
    none

  • 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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