1/35+1/63+1/99+1/143 简便计算

1/35+1/63+1/99+1/143 简便计算
1/35+1/63+1/99+1/143 简便计算

1/35+1/63+1/99+1/143 简便计算
1/35+1/63+1/99+1/143
=1/(5×7)+1/(7×9)+1/(9×11)+1/(11×13)
=1/2×(1/5-1/7)+1/2×(1/7-1/9)+1/2×(1/9-1/11)+1/2×(1/11-1/13)
=1/2×(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)
=1/2×(1/5-1/13)
=1/2×(13/65-5/65)
=1/2×8/65
=4/65

原式=1/1*3+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)
=1/2(1-1/13)=6/13

=1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)=1/2(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)=1/2*(1/5-1/13)=
4/65