1/(1*3)+1/(3*5)+1/(5*7)+.......+1/(2005*2007) 此题怎解
參考答案:答：1/(1*3)+1/(3*5)+1/(5*7)+.......+1/(2005*2007)
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+......+1/2(1/2005-1/2007)
=1/2(1-1/3+1/3-1/5+1/5-1/7+......+1/2005-1/2007)
=1/2(1-1/2007)
=1/2×2006/2007
=1003/2007
