Required Appropriate formulae for splitting values

Question

Here's my split

If single user 100%

If double user 75% 25%

If three user 60% 30% 10%

How can calculate for 4th and subsequent users, Kindly give me formulae to calculate this

Answer 1

Here's a hint for a possible method to extend those ratios: Note the 75 - 25 % is a 3:1 ratio. The 60 - 30 -10 % is a 6:3:1 ratio. Look at the sequence {1,3,6}. 3 = 1 + 2 and 6 = 3 + 3, so the second term is found by adding 2 to the first term, and the third term is found by adding 3 to the second term. A way to proceed would be to add 4 to the last term to get {1,3,6,10} giving ratios of 10:6:3:1 which corresponds to 50% 30% 15% 5%. This sequence can be continued as a well-known sequence called the triangular numbers.