Question

三分之一加一十五分之二加三十五分之二加六十三分之一加九十九分之七等于多少的算术步骤

Answer 1

那等于1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
=1/2 *（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）
=5/11

1/1*3是一乘以三的积分之一，其他类推

Answer 2

1/3+2/15+2/35+1/63+7/99
=1/3+1/63+7/99+2/15+2/35
=1/3+1/63+7/99+1/3-1/5+1/5-1/7
=1/3+1/63+7/99+1/3-1/7
=2/3+1/63+7/99-1/7
=2/3-1/7+1/63+7/99
=14/21-3/21+1/63+7/99
=11/21+1/63+7/99
=33/63+1/63+7/99
=34/63+7/99
=1/9*(34/7+7/11)
=1/9*(34*11/7+7*7/7*11)
=1/9*(374/77+49/77)
=1/9*423/77
=423/693
=47/77