已知数列{log2 (an-1)}为等差数列,且a1=3 a3=9 (1)求an (2)证明1/（a2-a1)+1/(a3
问题描述：
已知数列{log2 (an-1)}为等差数列,且a1=3 a3=9 (1)求an (2)证明1/（a2-a1)+1/(a3
an已经求出,an=2^n +1
(2)证明1/（a2-a1)+1/(a3-a2)+…+1/a(n+1)-an
答
1/（a2-a1)+1/(a3-a2)+…+1/a(n+1)-an
=1/2+1/2^2+…+1/2^n
=1/2+1/2^2+…+1/2^n+1/2^n-1/2^n
=1-1/2^n1/a(n+1)-an为什么成了1/2^n+1/2^n-1/2^n？1/2^n-1/2^n不是等于零吗？1/2^n-1/2^n是怎么来的？+0