作业帮2．计算：
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/05/01 05:49:28
2．计算：
(1) 2/3 + 1/3 + 1/5 + 2/15 + 2/21 + 1/14 + 1/18
= (2/3 + 1/3) + (1/5 + 2/15) + (2/21 + 1/14) + 1/18
= 1+ 1/3 + 1/6 +1/18
= 14/9
(2) 1/n(n+1)(n+2)(n+3)=1/3*[1/n(n+1)(n+2)-1/(n+1)(n+2)(n+3)]
1/1*2*3*4+1/2*3*4*5+.+1/7*8*9*10
=1/3*(1/1*2*3-1/2*3*4+1/2*3*4-1/3*4*5+.+1/7*8*9-1/8*9*10)
=1/3*(1/1*2*3-1/8*9*10)
=119/2160
= (2/3 + 1/3) + (1/5 + 2/15) + (2/21 + 1/14) + 1/18
= 1+ 1/3 + 1/6 +1/18
= 14/9
(2) 1/n(n+1)(n+2)(n+3)=1/3*[1/n(n+1)(n+2)-1/(n+1)(n+2)(n+3)]
1/1*2*3*4+1/2*3*4*5+.+1/7*8*9*10
=1/3*(1/1*2*3-1/2*3*4+1/2*3*4-1/3*4*5+.+1/7*8*9-1/8*9*10)
=1/3*(1/1*2*3-1/8*9*10)
=119/2160