Question

一道数学题，高手帮帮忙，急求答案！！！！

1/1*2*3+1/2*3*4+1/3*4*5+……+1/98*99*100=？
各位拜托了！
1/1×2×3+1/2×3×4+1/3×4×5+……+1/98×99×100=？
真的很急！！！！！！

Answer 1

因为
1/n(n+1)(n+2)=[1/n(n+1)-1/(n+1)(n+2)]/2

所以
1/1x2x3 + 1/2x3x4 +1/3x4x5 + … + 1/n(n+1)(n+2)
=[和1/n(n+1)-和1/(n+1)(n+2)]/2
=[1-1/(n+1)-1/2+1/(n+2)]/2
=1/4-1/2(n+1)(n+2)

同理
1/n(n+2)=[1/n-1/(n+2)]/2
1/1x3 + 1/2x4 + 1/3x5 … + 1/n(n+2)
=[1+1/2-1/(n+1)-1/(n+2)]/2
=3/4-1/2(n+1)-1/2(n+2)
代入即可得
3/4-1/2*99-1/2*100
=4949/19800

这种题目你可以到sina那里去看看

很多题目解得好有技巧

Answer 2

4949/19800
1/(n*(n+1)*(n+2))=1/2n -1/(n+1)+1/2(n+2)

Answer 3

4949/19800

Answer 4

4949/19800

Answer 5

一共8850