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已知0已知0已知0lim(a^n+b^n)^1/n=lim{(b^n)[(a/b)^n+1]}^(1/n)=lim(b^n)^(1/n)*lim[(a/b)^n+1]^(1/n)∵0

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lim(a^n+b^n)^1/n
=lim{(b^n)[(a/b)^n+1]}^(1/n)
=lim(b^n)^(1/n)*lim[(a/b)^n+1]^(1/n)
∵ 0