lim(a^n+b^n+c^n)^1/n=？？ n趋近与无穷大

原式=lim e^ln[(a^n+b^n+c^n)^1/n]
=lim e^[1/n*ln(a^n+b^n+c^n)]
现在求1/n*ln(a^n+b^n+c^n)的极限
lim 1/n*ln(a^n+b^n+c^n)
=lim ln(a^n+b^n+c^n)/n
=lim [(a^n*lna+b^n*lnb+c^n*lnc)/(a^n+b^n+c^n)]/1 罗比达法则
=lim (a^n*lna+b^n*lnb+c^n*lnc)/(a^n+b^n+c^n)
不妨设a是a是最大的，分子分母同时除以a^n
=lim [lna+(b/a)^n+(c/a)^n]/[1+(b/a)^n+(c/a)^n]
=lna

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
2楼大哥，别误导人家！1楼正解。取a、b、c中最大的那个数。设极限为m=max〔a，b，c〕
原式=lim e^ln[(a^n+b^n+c^n)^1/n]
=lim e^[1/n*ln(a^n+b^n+c^n)]
现在求1/n*ln(a^n+b^n+c^n)的极限
lim 1/n*ln(a^n+b^n+c^n)
=lim ln(a^n+b^n+c^n)/n
=lim [(a^n*lna+b^n*lnb+c^n*lnc)/(a^n+b^n+c^n)]/1 罗比达法则
=lim (a^n*lna+b^n*lnb+c^n*lnc)/(a^n+b^n+c^n)
不妨设a是a是最大的，分子分母同时除以a^n
=lim [lna+(b/a)^n+(c/a)^n]/[1+(b/a)^