14 out of 15 times 7 out of 17 times 5 out of 28 times 17

14 out of 15 times 7 out of 17 times 5 out of 28 times 17

14 out of 15 times 7 out of 17 times 5 out of 28 times 17
14/15 × 7/17 × 5/28 × 17
Original formula = (14 / 15 × 5 / 28) × (7 / 17 × 17)
= 1/6 × 7
=1 and 1 / 6

Calculate 1 / 11 * 13 * 15 + 1 / 13 * 15 * 17 + 1 / 15 * 17 * 19 +. 29 * 31 * 33 =?
1/11*13*15 +1/13*15*17 +1/15*17*19+.29*31*33=?
1/11*13*15 +1/13*15*17 +1/15*17*19+.1/29*31*33=?

1/11*13*15 +1/13*15*17 +1/15*17*19+.1/29*31*33=?
=(1/11*13-1/13*15+1/13*15-1/15*17 +1/15*17.1/29*31-1/31*33)*1/4
=（1/11*13-1/31*33)*1/4
The following is easy to do, which is a problem of item splitting

1 / 11 * 13 * 15 + 1 / 13 * 15 * 17 +... + 1 / 29 * 31 * 33
How to solve this problem?

=1/8*(1/11-1/13-1/13+1/15 +1/13-1/15-1/15+1/17 +...+1/29-1/31-1/31+1/33)
The middle of all offset, leaving only the first and last four
1/8*（1/11-1/13-1/31+1/33）=10/13299

7 / 12 times 11 plus 7 / 12 recursive equation calculation

7 / 12 times 11 plus 7 / 12
=7/12×(11+1)
=7/12×12
=7