1/1×3+1/3×5+1/5×7+........＋1/99×101＝

来源：百度知道 编辑：UC知道 时间：2024/06/23 12:47:19

1/1×3=1/2*(1/1-1/3)
1/3×5=1/2*(1/3-1/5)
...
1/99×101=1/2(1/99-1/101)

所以1/1×3+1/3×5+1/5×7+........＋1/99×101＝1/2×（1/1-1/3＋1/3-1/5＋。。＋1/99-1/101）＝1/2×（1-1/101）＝50/101

1/1×3+1/3×5+1/5×7+........＋1/99×101
=(1-1/3)÷2+(1/3-1/5)÷2+(1/5-1/7)÷2+……+(1/99-1/101)÷2
=(1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)÷2
=(1-1/101)÷2
=100/101÷2
=50/101

1/1×3+1/3×5+1/5×7+........＋1/99×101
＝(1+2/1)+(1+2/3)+(1+2/5)+(1+2/7)+......+(1+2/101)
=1*51+2(1+1/3+1/5+1/7+...+1/101)
=51+2
=53

=1/2*(1-1/3)+1/2*(1/3-1/5)+...+1/2*(1/99-1/101)
=1/2-1/202
=50/101

原式=1/2(1-1/3+1/3-1/5+1/5-1/7+....1/99-1/100)=1/2(1-1/100)=99/200