设备安装专业:lim[(1-1/4)(1-1/9)...(1-1/(n+1)^2]=?

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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

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