1/1×4+1/4×7+1/7×10+1/10×13+···+1/2008×2011 =

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 09:48:47
1/1×4+1/4×7+1/7×10+1/10×13+···+1/2008×2011=1/1×4+1/4×7+1/7×10+1/10×13+···+1/2008×2011=1/1×4+1/4×7+1/

1/1×4+1/4×7+1/7×10+1/10×13+···+1/2008×2011 =
1/1×4+1/4×7+1/7×10+1/10×13+···+1/2008×2011 =

1/1×4+1/4×7+1/7×10+1/10×13+···+1/2008×2011 =
1/(1×4)+1/(4×7)+1/(7×10)+1/(10×13)+···+1/(2008×2011)
=(1-1/4)/3+(1/4-1/7)/3+...+(1/2008-1/2011)/3
=(1-1/4+1/4-1/7+...+1/2008-1/2011)/3
=(1-1/2011)/3
=670/2011