已知x1=1,x2=1+x1/(x1+1),Xn=1+1/(1+Xn-1) 求数列Xn的极限

设 :lim Xn = A
n→∞
根据,lim Xn = lim {1 + 1/[1 + X(n-1)]}
n→∞ n→∞
得到：A = 1 + 1/(1 + A)
即：A(1 + A) = 1 + A + 1
A² = 2
所以,A = 根号2.