求下列数列的极限:lim(n→∞) [n*(1-1/3)*(1-1/4)*……*(1-1/n+2)]
问题描述:
求下列数列的极限:lim(n→∞) [n*(1-1/3)*(1-1/4)*……*(1-1/n+2)]
答
n*(1-1/3)*(1-1/4)*……*(1-1/n+2)] =n*2/3*3/4*4/5*.*(n+1)/(n+2)=n*2/(n+2)=2n/(n+2)lim(n→∞) [n*(1-1/3)*(1-1/4)*……*(1-1/n+2)]=lim(n→∞) [2n/(n+2)]=2*lim(n→∞) [n/(n+2)]=2*1=2