llsa2003
春芽
共回答了16个问题采纳率:81.3% 举报
2^n=(2-1)*2^n
=2*2^n-2^n
=2^(n+1)-2^n
=[2^(n+1)-1]-(2^n-1)
所以(2^n)/{(2^n-1)[2^(n+1)-1]}
=[2^(n+1)-1]/{(2^n-1)[2^(n+1)-1]}-(2^n-1)//{(2^n-1)[2^(n+1)-1]}
=1/(2^n-1)-1/[2^(n+1)-1]
所以相加=1/(2-1)-1/(4-1)+1/(4-1)-1/(8-1)+……+1/(2^n-1)-1/[2^(n+1)-1]
=1-1/[2^(n+1)-1]
=[2^(n+1)-2]/[2^(n+1)-1]
1年前
1