Question

1×2×3×4分之3+2×3×4×5分之3+……+17×18×19×20分之3

Answer 1

1/n(n+1)(n+2)(n+3)
=1/2{1/n - 1/(n+3) + 1/(n+2)-1/(n+1)}

1×2×3×4分之3+2×3×4×5分之3+……+17×18×19×20分之3
=3/2*(1+1/3-1/2-1/4 +1/2+1/4-1/3-1/5+...+1/17+1/19-1/18-1/20)
=3/2*(1-1/20)
=3/2*19/20
=57/40
【参考：http://zhidao.baidu.com/question/186456720.html】

Answer 2

=(1/1×2×3-1/2×3×4)+(1/2×3×4-1/3×4×5)+……+(1/17×18×19-1/18×19×20)
= 1/1×2×3-1/18×19×20
=1/6-1/6840
=1139/6840

追答

【附注】a/b表示b分之a

那位大神，你的答案真心无语