已知各项均为正数的数列{an}满足a0=1/2,an=a(n-1)+(1/n^2)*(a(n-1))^2其中n=1,2,3...1 求a1 a22 求证 1/a(n-1)-1/an
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![已知各项均为正数的数列{an}满足a0=1/2,an=a(n-1)+(1/n^2)*(a(n-1))^2其中n=1,2,3...1 求a1 a22 求证 1/a(n-1)-1/an](/uploads/image/z/11625500-20-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%BA%E6%AD%A3%E6%95%B0%E7%9A%84%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a0%3D1%2F2%2Can%3Da%28n-1%29%2B%281%2Fn%5E2%29%2A%28a%28n-1%29%29%5E2%E5%85%B6%E4%B8%ADn%3D1%2C2%2C3...1+%E6%B1%82a1+a22++%E6%B1%82%E8%AF%81+1%2Fa%28n-1%29-1%2Fan)
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