1/ (1×4 )+ 1/ (4×7)+1/(7×10)+1/(10×13)+.+1/(2008×2011)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/28 08:37:51
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)×1/3+(1/4-1/7)×1/3+(1/7-`/10)×1/3+(1/2008-1/2011)×1/3
=1/3×(1-1/4+1/4-1/7+1/7-`/10+.+1/2008-1/2011)
=1/3×(1-1/2011)
=1/3×2010/2011
=670/2011
=(1-1/4)×1/3+(1/4-1/7)×1/3+(1/7-`/10)×1/3+(1/2008-1/2011)×1/3
=1/3×(1-1/4+1/4-1/7+1/7-`/10+.+1/2008-1/2011)
=1/3×(1-1/2011)
=1/3×2010/2011
=670/2011
1/ (1×4 )+ 1/ (4×7)+1/(7×10)+1/(10×13)+.+1/(2008×2011)
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