Lim[(x+1)(x^2+1)·……·(x^n+1)]/([nx)^n+1]^(n+1)/2

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Lim[(x+1)(x^2+1)·……·(x^n+1)]/([nx)^n+1]^(n+1)/2
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Lim[(x+1)(x^2+1)·……·(x^n+1)]/([nx)^n+1]^(n+1)/2
Lim[(x+1)(x^2+1)·……·(x^n+1)]/([nx)^n+1]^(n+1)/2

Lim[(x+1)(x^2+1)·……·(x^n+1)]/([nx)^n+1]^(n+1)/2
原式 = [ x^(n*(n+1)/2) +.]/ [n^(n*(n+1)/2) * x^(n*(n+1)/2) + .]
= 1/ n^(n*(n+1)/2)