作业帮1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/04/29 08:22:24
1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么
1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013)
=1/2 x[2/(1x3)+2/(3x5)+2/(5x7)+.+2/(2011x2013)]
=1/2 x[1-1/3+1/3-1/5+1/5-1/7+.+1/2011-1/2013]
=1/2 x[1-1/2013]
=1/2 x[2012/2013]
=1006/2013
再问： 能解释一下吗????
再答： 是裂项抵消法 2/(1x3)=1/1 -1/3 2/(3x5)=1/3-1/5 2/(5x7)=1/5-1/7
=1/2 x[2/(1x3)+2/(3x5)+2/(5x7)+.+2/(2011x2013)]
=1/2 x[1-1/3+1/3-1/5+1/5-1/7+.+1/2011-1/2013]
=1/2 x[1-1/2013]
=1/2 x[2012/2013]
=1006/2013
再问： 能解释一下吗????
再答： 是裂项抵消法 2/(1x3)=1/1 -1/3 2/(3x5)=1/3-1/5 2/(5x7)=1/5-1/7
1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么
1/1x3+1/3x5+1/5x7.1/2009x2010+1/2011x2013
1/1x3+1/3x5+1/5x7+…+1/2011x2013是多少?
1分之1x3+1分之3x5+1分之5x7+.+1分之2011x2013
1X3分之一+3X5分之一+5X7分之一…+2011X2013分之一
计算：1/1x3+1/3x5+1/5x7+1/7x9+……+1/2011x2013
计算：1/1x3+1/3x5+1/5x7+...1/2009x2011+1/2011×2013
1/1X3+1/3X5+1/5X7...1/17X19+1/19X21=
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=?
1/1x3+1/3x5+1/5x7+……+1/99x101
1/1x3+1/3x5+1/5x7+.+1/2009x2011=
1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算.