高等数学证明数列收敛和求出极限

a(n+1)=[an/(1+an)]^(1/2)|an| > 0{an} 递减=> lim(n->∞)an existslim(n->∞)a(n+1)=lim(n->∞)[an/(1+an)]^(1/2)L= (L/(1+L))^(1/2)L^2(1+L) = LL(L^2+L -1) =0L = (-1+√5)/2lim(n->∞)an =L =(-1+√5)/2不对啊 令f(x)=(x/1+x)^1/2求导后是恒大于0的函数，单调递增啊。 怎么能递减你做的没问题？