lim [n(1-1/3)(1-1/4)(1-1/5)…(1-1/n+2)]等于多少？n→∞

熱心網友

lim [n(1-1/3)(1-1/4)(1-1/5)…(1-1/n+2)]n→∞ =lim [n*(2/3)*(3/4)*(4/5)*…*n/(n+1)*(n+1)/(n+2)]=lim [(2n)/(n+2)]=lim [2/(1+2/n)]=2