(1/2+1/3+…+1/2011)(1+1/2+…+1/2010)-(1+1/2+…+1/2011)(1/2+1/3+…+1/2010)计算别做错啦

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 15:49:28

(1/2+1/3+…+1/2011)(1+1/2+…+1/2010)-(1+1/2+…+1/2011)(1/2+1/3+…+1/2010)计算别做错啦
(1/2+1/3+…+1/2011)(1+1/2+…+1/2010)-(1+1/2+…+1/2011)(1/2+1/3+…+1/2010)计算
别做错啦

(1/2+1/3+…+1/2011)(1+1/2+…+1/2010)-(1+1/2+…+1/2011)(1/2+1/3+…+1/2010)计算别做错啦
(1/2+1/3+…+1/2011)(1+1/2+…+1/2010)
-(1+1/2+…+1/2011)(1/2+1/3+…+1/2010)
= [(1/2+1/3+…+1/2010) +1/2011] [1+ (1/2+…+1/2010)]
-[1+ (1/2+…+1/2010) + 1/2011](1/2+1/3+…+1/2010)
= 2012/2011(1/2+1/3+…+1/2010)+(1/2+1/3+…+1/2010)^2 + 1/2010(2011)
- 2012/2011(1/2+…+1/2010) - (1/2+…+1/2010)^2
= 1/2010(2011)
=1/4042110 #