证明1/(2^2-1)+1/(2^3-1)+……+1/(2^n-1)有人说有五种方法，我已经得到三种

网友回答

consider
for n>=31/(2^n-1) an = 1/[2^(n+1) -1]
a1=1/3
1/(2^2-1)+1/(2^3-1)+……+1/(2^n-1)
=Sn=a1+a2+..+an
= 1/3 + 1/(2^3-1)-1/(2^4-1)+...+1/(2^n-1)
======以下答案可供参考======
供参考答案1:
1/(2^2-1)+1/(2^3-1)+……+1/(2^n-1)
=(1/2^2)*(1-(1/2)^n)/(1-1/2)