1/3+1/15+1/35+1/63+1/99+1/143=? 重要讲方法.

=1/(1*3)+1/(3*5)+1/(5*7)+...+1/(11*13)
=0.5*(3-1)/(1*3)+0.5*(5-3)/(3*5)+...+0.5*(13-11)/(11*13)
=0.5*(1-1/3)+0.5*(1/3-1/5)+...+0.5*(1/11-1/13)
=0.5*(1-1/3+1/3-1/5+...+1/11-1/13)
=0.5*(1-1/13)
=6/13

不会

3=1*3 15=3*5 35=5*7 63=7*9 99=9*11 143=11*13
你可以发现相乘的两个数都差2
所以裂项相消
原式=（1-1\3+1\3-1\5+1\5-1\7+1\7-1\9+1\9-1\11+1\11-1\13)\2=6\13

1/3+1/15+1/35+1/63+1/99+1/143
=（1-1/3）/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+（1/9-1/11）/2+（1/11-1/13）/2
=（1-1/13）/2
=6/13