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The value of lim(n->oo) [(1+1/n^2)(1+2^2...

The value of `lim_(n->oo) [(1+1/n^2)(1+2^2/n^2)...(1+n^2/n^2)]^(1/n)`

Text Solution

Verified by Experts

The correct Answer is:
`2e^((pi-4)//2)`
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The value of lim_ (n rarr oo) [(1+ (1) / (n ^ (2))) (1+ (2 ^ (2)) / (n ^ (2))) ... (1+ (n ^ (2)) / (n ^ (2)))] ^ ((1) / (n))

Knowledge Check

  • The value of lim_(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+(n-1)^(2))] is :

    A
    `(pi)/(2)`
    B
    `(pi)/(4)`
    C
    `pi`
    D
    `-(pi)/(4)`

  • The value of lim_( n to oo) ((1)/(n) + (n)/((n+1)^2) + (n)/( (n+2)^2) + ...+ (n)/( (2n-1)^2) ) is

    A
    `1`
    B
    `1//3`
    C
    `1//2`
    D
    `3//2`

  • The value of lim_(x to oo) (1 + 2 + 3 … + n)/(n^(2)) is

    A
    1
    B
    `(1)/(2)`
    C
    0
    D
    `(3)/(2)`

    • Similar Questions

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    The value of lim_(n rarr oo)(((2n)(2n+1)(2n+2)...(4n))^((1)/(n)))/((n)^(2+(1)/(n))) is

    The value of lim_ (n rarr oo) [(1) / (n) + (e ^ ((1) / (n))) / (n) + (e ^ ((2) / (n))) / (n) + .... + (e ^ ((n-1) / (n))) / (n)] is:

    lim_(n->oo) (1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}

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