1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么
问题描述：
1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么
答
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能解释一下吗????是裂项抵消法2/(1x3)=1/1 -1/32/(3x5)=1/3-1/52/(5x7)=1/5-1/7