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For each positive integer n , let yn=1...

For each positive integer `n` , let `y_n=1/n((n+1)(n+2). . . (n+n))^(1/n)` For `x in R` let `[x]` be the greatest integer less than or equal to `x` . If `(lim)_(n->oo)y_n=L` , then the value of `[L]` is ______.

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For each positive integer n, let j y_(n) =1/n ((n +1) (n +2) …(n +n) )^(1/n). For x in R, let [x] be the greatest integer less than or equal to x, If lim _( n to oo) y_(n) =L, then the value of [L] is "_________."

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Knowledge Check

  • If n in N , and [x] denotes the greatest integer less than or equal to x, then lim_(xrarrn)(-1)^([x]) is equal to.

    A
    1
    B
    -1
    C
    0
    D
    none of these

  • For a positive integer n , let a(n) = 1+ 1/2 + 1/3 +…+ 1/(2^(n)-1) : Then

    A
    `a (100) lt 100`
    B
    `a (200 ) lt 200`
    C
    `a(200) gt 100`
    D
    `a(100) lt 200`

  • Let f(n) =[1/3 + (3n)/100]n , whre [x] denotes the greatest integer less than or equal to x. Then sum_(n=1)^(56) f(n) is equal to

    A
    689
    B
    1399
    C
    1287
    D
    56

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