求函数的极限:lim(1^n+2^n+3^n+4^n)^1/n,当n→∞时的极限.(不用夹逼准则解)
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求函数的极限:lim(1^n+2^n+3^n+4^n)^1/n,当n→∞时的极限.(不用夹逼准则解)
求函数的极限:lim(1^n+2^n+3^n+4^n)^1/n,当n→∞时的极限.(不用夹逼准则解)
求函数的极限:lim(1^n+2^n+3^n+4^n)^1/n,当n→∞时的极限.(不用夹逼准则解)
(1^n+2^n+3^n+4^n)^1/n
=e^{ln[(1^n+2^n+3^n+4^n)^1/n]}
=e^{(1/n)*ln(1^n+2^n+3^n+4^n)}
lim(n->∞) (1/n)*ln(1^n+2^n+3^n+4^n) (用咯比达法则)
=lim(n->∞) [(ln1*1^n+ln2*2^n+ln3*3^n+ln4*4^n)/(1^n+2^n+3^n+4^n)]
=lim(n->∞) [(ln1*(1/4)^n+ln2*(2/4)^n+ln3*(3/4)^n+ln4)/((1/4)^n+(2/4)^n+(3/4)^n+1)]
=ln4
所以原式=lim(n->∞) e^{(1/n)*ln(1^n+2^n+3^n+4^n)}
=e^{lim(n->∞) (1/n)*ln(1^n+2^n+3^n+4^n)}
=e^(ln4)
=4
求函数的极限:lim(1^n+2^n+3^n+4^n)^1/n,当n→∞时的极限.(不用夹逼准则解)
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