求和:1/2+3/4+5/8+……+2n-1/2n 1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+……+n)
问题描述:
求和:1/2+3/4+5/8+……+2n-1/2n 1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+……+n)
答
1/2+3/4+5/8+……+2n-1/2n
题不对吧?
5/8不满足后面的式子
1/(1+2+3+……+n)=1/[n(n+1)/2]=2/(n+1)n=2[1/n-1/(n+1)]
所以原式为
2[1+1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/n+1]
=2[2-1/n+1]
=4-2/n+1