1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80=?要简便算法啊,

分组,列项
1/3=1/2*(1-1/3)
1/15=1/2*(1/3-1/15)
.
1/8=1/2*(1/2-1/4)
1/24=1/2*(1/4-1/6)
.
1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80
=(1/3+1/15+1/35+1/63)+(1/8+1/24+1/48+1/80)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)+1/2*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)
=1/2*(1-1/9+1/2-1/10)
=1/2*58/45
=58/90

1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80
=1/(1*3)+1/(2*4)+1/(3*5)+1/(4*6)+1/(5*7)+1/(6*8)+1/(7*9)+1/(8*10)
=1/2 (1-1/3 + 1/2-1/4 + 1/3-1/5 + 1/4-1/6 + 1/5-1/7 + 1/6-1/8 + 1/7-1/9 + 1/8-1/10)
=1/2 (1+1/2-1/9-1/10)
=1/2 * 58/45
= 29/45