初一数学题（由于分数无法输入，只好用/代替）

1/1×2+1/2×3+1/3×4……1/99×100
= (1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)
=1-1/100
=99/100

1/1×3+1/3×5+1/5×7……1/99×100
=1/2[(1-1/3)+(1/3-1/5)+(1/5-1/7)……+(1/97-1/99)]+(1/99-1/100)
=1/2(1-1/99)+1/99-1/100
=50/99-1/100
=4901/9900

1/1×2+1/2×3+1/3×4……1/99×100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100
=1-1/100
=99/100

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

1/1×2+1/2×3+1/3×4……1/99×100
=1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100

=1-1/100

=99/100

1/1×3+1/3×5+1/5×7……1/99×100

=1/2×(2/1×3＋2/3×5+2/5×7……2/99×100）

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

=1/2×(1-1/100)

=99/200

1/1*2=1-1/2
1/2×3=1/2-1/3
以