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1/1x6+1/6x11+1/11x16+...+1/2001x2009=?
题目详情
1/1x6+1/6x11+1/11x16+...+1/2001x2009=?
▼优质解答
答案和解析
1/1x6+1/6x11+1/11x16+...+1/2001x2009 (应该是2006 而不是2009)
=(1-1/6)÷5+(1/6-1/11)÷5+(1/11-1/16)÷5+……+(1/2001-1/2006)÷5
=[(1-1/6)+(1/6-1/11)+(1/11-1/16)+……+(1/2001-1/2006)]÷5
=(1-1/6+1/6-1/11+1/11-1/16+……+1/2001-1/2006)÷5
中间互相抵消
=(1-1/2006)÷5
=2005/2006÷5
=401/2006
=(1-1/6)÷5+(1/6-1/11)÷5+(1/11-1/16)÷5+……+(1/2001-1/2006)÷5
=[(1-1/6)+(1/6-1/11)+(1/11-1/16)+……+(1/2001-1/2006)]÷5
=(1-1/6+1/6-1/11+1/11-1/16+……+1/2001-1/2006)÷5
中间互相抵消
=(1-1/2006)÷5
=2005/2006÷5
=401/2006
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