1 1 1 1 1
----+----+----+----+…加---------
1×2 2×3 3×4 4×5 99×100
=1-1/2+1/2-1/3+1/3-1/4.
=1-1/100
=99/100
1 1 1 1
------+------+------+------
10×12 12×14 14×16 16×18
=1/4(1/5-1/6+1/6-1/7+..+1/8-1/9)
=1/4*(1/5-1/9)
=1/45
1 1 1 1 1
----+----+----+----+…加---------
1×2 2×3 3×4 4×5 99×100
=1-1/2+1/2-1/3+1/3-1/4.
=1-1/100
=99/100
1 1 1 1
------+------+------+------
10×12 12×14 14×16 16×18
=1/4(1/5-1/6+1/6-1/7+..+1/8-1/9)
=1/4*(1/5-1/9)
=1/45