聚飞光电公司简介:lim[(1-1/4)(1-1/9)...(1-1/(n+1)^2]=?

来源:百度文库 编辑:高校问答 时间:2024/10/04 16:11:54

lim[(1-1/4)(1-1/9)...(1-1/(n+1)^2]
=lim(1/2*3/2*2/3*4/3*3/4*5/4...*n/(n+1)*(n+2)/(n+1)
=lim(1/2*2/3*3/4*...*n/(n+1)*3/2*4/3*5/4*...(n+2)/(n+1)
=lim(1/(n+1)*(n+2)/2)
=lim(n+2)/(2*(n+1))
=1/2