21-4/3-4/15-4/35-4/63-4/99-4/143-4/195
问题描述：
21-4/3-4/15-4/35-4/63-4/99-4/143-4/195
答
21-4/3-4/15-4/35-4/63-4/99-4/143-4/195
= 21 - 4/(1×3) - 4/(3×5) - 4/(5×7) - 4/(7×9) - 4/(9×11) - 4/(11×13) - 4/(13×15)
= 21 + (2/3 - 2) + (2/5 - 2/3) + (2/7 - 2/5) + (2/9 - 2/7) + (2/11-2/9) + (2/13-2/11) + (2/15-2/13)
= 21 - 2 + 2/15
= 19 + 2/15
等于19又15分之2
答
21-4/3-4/15-4/35-4/63-4/99-4/143-4/195
=21-2×（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15）
=21-2×(1-1/15)
=21-2+2/15
=19又2/15