Question

已知数列{an}满足an+1=an2-2(n∈N*),且a1=a,a2015=b(a,b>2)则a1a2a3……a2014=________

等式左边是第n+1项，右边是第n项的平方减2

Answer 1

Answer 2

令a1a2a3……a2014=x显然x>0,则 由题意可得如下两点①an+1  +2=an^2②an+1   -2=an^2-4=(an  -2)(an   +2),那么

故x=根号下（b^2 -4)/(a^2 -4)