Question

定义max{a,b}表示实数a,b中的较大的.已知数列{an}满足a1=a(a>0),

Answer 1

写出a(n)的前几项

a(1) = a, a(2) = 1, a(3) = 4/a, a(4) = 8/a (if a < 2) or 4(if a >= 2),

a(5) = 4(if a < 2) or 2a(if a >= 2), a(6) = a, a(7) = 1, ... 以后一直循环下去

周期是5

a(2014) = a(4), 两种情况解出来 a=2

所以数列就是 2,1,2,4,4,2,1,2,4,4,...

S(2014) = S(2015) - a(2015) = 2015/5*(2+1+2+4+4) - 4 = 5235