高微(收斂數列)

|x_(n+1)-x_n| ≦ |x_n-x_{n-1}|/√2 ≦ |x_{n-1}-x_{n-2}|/2
　　 ≦ |x_2-x_1|/2^{(n-1)/2}

|x_{n+k}-x_n| ≦ |x_{n+k}-x_{n+k-1}|+...+|x_{n+1}-x_n|
　　 ≦ |x_2-x_1|(1/2{(n+k-2)/2}+...+1/2^{(n-1)/2})
　　 ≦ (|x_2-x_1|/2^{(n-1)/2})/(1-1/√2)

當 n→∞, k>0, |x_{n+k}-x_n|→0, 即 {x_n} 為一Cauchy sequence.

故 {x_n} 收斂.