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也不一定要推公式,用误差也可以

Posted by whosyourdaddy at 2010-06-20 23:18:10 on Problem 2601
a[k+1]=2(a[k]+c[k])-a[k-1];
假设真实a[1]=x, 现假设a[1]=0, 那么误差就是x

用这个误差带进上式
a[2]=2(x+c[1])-a[0];
a[2]的误差就是2x

a[3]=2(2x+c[2])-x;
a[3]的误差是3x

可以发现
a[k]的误差是kx

所以,a[1]=0和最开始的式子推到a[n+1],再和真实的a[n+1]求误差,除以n+1,就是a[1]的值

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