求极限lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)=_____

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求极限lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)=_____
求极限lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)=_____

求极限lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)=_____
平方差
=(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]
中间约分
=(1/2)[(n+1)/n]
=(n+1)/2n
=(1+1/n)/2
所以极限=1/2

lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)=0

1/n^2 = (n-1)(n+1)/n^2
原式 = 1/2 * (n+1)/n
=1/2

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