证明,lim(a^n/n!)=0 n-∞

题目

证明,lim(a^n/n!)=0 n-∞

答案

令N= [a]+1,则当n>N时,有n>a,且a/(N+1)N时,a^n/n!
=a/1 * a/2 * ...* a/N * a/(N+1) * ...a/n