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

For each positive integer `n` , let `y_n=1/n((n+1)(n+2)dot(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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