1/2×2/3+1/3×2/4+1/4×2/5+……＋1/99×2/100 计算

来源：学生作业帮助网编辑：六六作业网时间：2024/05/16 06:32:25

1/2×2/3+1/3×2/4+1/4×2/5+……＋1/99×2/100计算1/2×2/3+1/3×2/4+1/4×2/5+……＋1/99×2/100计算1/2×2/3+1/3×2/4+1/4×2/

1/2×2/3+1/3×2/4+1/4×2/5+……＋1/99×2/100 计算
1/2×2/3+1/3×2/4+1/4×2/5+……＋1/99×2/100 计算

1/2×2/3+1/3×2/4+1/4×2/5+……＋1/99×2/100 计算
原式=2×（1/2×1/3+1/3×1/4+1/4×1/5+……+1/99×1/100）
=2×（1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100）
=2×（1/2-1/100）
=2×49/100=49/50

1/n x 1/(n+1) = 1/n - 1/(n+1)
所以，原式=2×[1/2-1/3+1/3-1/4+1/4-1/5+……＋1/99-1/100]
=2×[1/2-1/100]
=2×49/100
=49/50

原式=2*（1/2-1/3+1/3-1/4…+1/99-1/100）=2*(1/2-1/100)=0.98

1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1,2,3,4, 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1、2、3、4 1+2+3×4 1,2,3,4 1+2+3+4+.