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lim(a^n+b^n+c^n)^1/n=?n趋近与无穷大
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lim(a^n+b^n+c^n)^1/n=?n趋近与无穷大
▼优质解答
答案和解析
(a^n+b^n+c^n)^1/n
=exp{(1/n)In(a^n+b^n+c^n)}
lim(1/n)In(a^n+b^n+c^n)
=lim[In(a^n+b^n+c^n)]/n
=lim 1/(a^n+b^n+c^n)
=0
lim(a^n+b^n+c^n)^1/n
=e^lim(1/n)In(a^n+b^n+c^n)
=e^0
=1
=exp{(1/n)In(a^n+b^n+c^n)}
lim(1/n)In(a^n+b^n+c^n)
=lim[In(a^n+b^n+c^n)]/n
=lim 1/(a^n+b^n+c^n)
=0
lim(a^n+b^n+c^n)^1/n
=e^lim(1/n)In(a^n+b^n+c^n)
=e^0
=1
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