Question

三分之一加十五分之一加三十五分之一加六十三分之一加九十九分之一加一百四十三分之一简便计算

Answer 1

1/3+1/15+1/35+1/63+1/99+1/143

=1/3+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)+1/(11×13)

=1/3+1/2×(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)

=1/3+1/2×(1/3-1/13)

=1/3+1/6-1/26

=1/2-1/26

=13/26-1/26

=12/26

=6/13