Is there a way to solve this problem easily ?

I want to find the initial increment for a mathematical serie of n values. All series have to go from 0 to 1.

With 3 values, for example, the initial increment is 0.3333333:

First value = 0 + (0*0.333333) = 0

Second value = first value + (1*0.333333) = 0.33333333

Third value = second value + (2*0.3333333) = 1

With 4 values, the initial increment is 0.1666666:

First value = 0 + (0*0.1666666) = 0

Second value = first value + (1*0.1666666) = 0.1666666

Third value = second value + (2*0.1666666) = 0.5

Fourth value = third value + (3*0.1666666) = 1

A big like for any answer helping to solve that problem without using brute force.