lim(n趋向于正无穷)[1-(1/2^2)][1-(1/3^2)].[1-(1/n^2)] 等于多少,
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lim(n趋向于正无穷)[1-(1/2^2)][1-(1/3^2)].[1-(1/n^2)] 等于多少,
![lim(n趋向于正无穷)[1-(1/2^2)][1-(1/3^2)].[1-(1/n^2)] 等于多少,](/uploads/image/z/17363257-25-7.jpg?t=lim%28n%E8%B6%8B%E5%90%91%E4%BA%8E%E6%AD%A3%E6%97%A0%E7%A9%B7%29%5B1-%281%2F2%5E2%29%5D%5B1-%281%2F3%5E2%29%5D.%5B1-%281%2Fn%5E2%29%5D+%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%2C)
lim[n->∞](1-1/2²)*...*(1-1/n²)
=lim[n->∞]((2²-1)/2²)*..*((n²-1)/n²)
=lim[n->∞]((2-1)(2+1)*(3-1)*(3+1)*...*(n-1)*(n+1)/(n!)²)
=lim[n->∞](n-1)!*(n+1)!/(2(n!)²)
=lim[n->∞](n+1)/(2n)
=1/2
=lim[n->∞]((2²-1)/2²)*..*((n²-1)/n²)
=lim[n->∞]((2-1)(2+1)*(3-1)*(3+1)*...*(n-1)*(n+1)/(n!)²)
=lim[n->∞](n-1)!*(n+1)!/(2(n!)²)
=lim[n->∞](n+1)/(2n)
=1/2
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