1 * 3:1 + 3 * 5:1 + 5 * 7:1 + 7 * 9:1 + 9 * 11:1 + 11 * 13:1 + 13 * 15:1 =? Simple calculation

1 * 3:1 + 3 * 5:1 + 5 * 7:1 + 7 * 9:1 + 9 * 11:1 + 11 * 13:1 + 13 * 15:1 =? Simple calculation

1 × 3 / 1 + 3 × 5 × 1 + 5 × 7 / 1 + 7 × 9 / 1 + 9 × 11 / 1 + 11 × 13 / 1 + 13 × 15 / 1
=(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)×(1/13-1/15)
=(1/2)×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=(1/2)×(1-1/15)
=1/2×14/15
=7/15