已知数列{an}中,a1=1,a2=0,对任意正整数n,m(n>m)满足 (an)^2-(am)^2=an-man+m,则a119_数学解答

已知数列{an}中,a1=1,a2=0,对任意正整数n,m(n>m)满足 (an)^2-(am)^2=an-man+m,则a119

人气：196 ℃　时间：2020-06-03 13:59:46

解答

(an)^2-(am)^2=an-man+m对任意正整数n,m(n>m)都成立,
不妨设n=119,m=1或2
(a119)^2-(a1)^2=a119-a119+1=1
(a119)^2-(a2)^2=a119-2a119+2=-a119+2
(a119)^2=2
(a119)^2+a119=2
无解.