lim(a^n+b^n+c^n)^1/n=?n趋近与无穷大_数学解答

lim(a^n+b^n+c^n)^1/n=?n趋近与无穷大

人气：487 ℃　时间：2020-04-06 14:18:35

解答

(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)=0lim(a^n+b^n+c^n)^1/n=e^lim(1/n)In(a^n+b^n+c^n)=e^0=1