Question

已知an=2^n/(2^n-1)(2^n+1 -1),求Sn

Answer 1

a(n) + [a(n+1)+a(n+2)+...+a(n+k-1)] = [a(n+1)+a(n+2)+...+a(n+k-1)] + a(n+k),

等式两边抵消掉[a(n+1)+a(n+2)+...+a(n+k-1)],得

a(n) = a(n+k)

当a(n) = a(n+k)对任意正整数n都成立时,说明{a(n)}是周期为k的周期数列.

希望对你能有所帮助.