如题所述
第1个回答 2013-12-04
1/(1×3)+1/(3×5)+1/(5×7)+.......+1/(1009×1011)
=½×(1-1/3)+½(1/3-1/5)+½(1/5-1/7)+.....+½(1/1009-1/1011)
=½(1-1/3+1/3-1/5+1/5-1/7+.....1/1009-1/1011)
=½(1-1/1011)
=½×1010/1011
=505/1011
仅供参考 祝你愉快
=½×(1-1/3)+½(1/3-1/5)+½(1/5-1/7)+.....+½(1/1009-1/1011)
=½(1-1/3+1/3-1/5+1/5-1/7+.....1/1009-1/1011)
=½(1-1/1011)
=½×1010/1011
=505/1011
仅供参考 祝你愉快
第2个回答 2013-12-04
1/1*3+1/3*5+1/5*7+......+1/1009*1011=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+.....+(1/2009-1/2011)]/2
=(1-1/2011)/2=1005/2011
=(1-1/2011)/2=1005/2011