xn > 2
(随便说句:这个序列不是单调的)
{x(n+1)-xn| = |1/xn - 1/x(n-1)|< |xn -x(n-1)|/4
于是也有:
{x(n+i+1)-x(n+i)||< |x(n+i) -x(n+i-1)|/4
< ...
< |x(n+1) -xn|/4^i
所以:仍给 n,m>0:
|x(n+m)-xn| x^2-2x -1 = 0,因为 x >=2,x = 1 + 根2.
xn > 2
(随便说句:这个序列不是单调的)
{x(n+1)-xn| = |1/xn - 1/x(n-1)|< |xn -x(n-1)|/4
于是也有:
{x(n+i+1)-x(n+i)||< |x(n+i) -x(n+i-1)|/4
< ...
< |x(n+1) -xn|/4^i
所以:仍给 n,m>0:
|x(n+m)-xn| x^2-2x -1 = 0,因为 x >=2,x = 1 + 根2.