记：
sn=(1-1/2^2)(1-1/3^2)……(1-1/n^2)
=(1-1/2)(1+1/2)*(1-1/3)(1+1/3)*……*(1-1/n)(1+1/n)
=(1/2)(3/2)(2/3)(4/3)……((n-1)/n)((n+1)/n)
=(1/2)((n+1)/n)
=(n+1) / 2n
故，
lim (1-1/2^2)(1-1/3^2)……(1-1/n^2)
=lim sn
=lim (n+1) / 2n
=lim (n+1)/n / 2n/n
=lim (1+(1/n)) / 2
=1/2
有不懂欢迎追问
an=(1/1/2^2)(1-1/3^2)...(1-1/n^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/n)(1+1/n)
=(1/2)(3/2)(2/3)(4/3)...((n-1)/n)((n+1)/n)
=(n+1)/(2n)
令n->∞得an->1/2
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