Given an item with a value of X, it has a 50% chance to split/double, so now we have two items, each with value X. They each have separate, and half the chance to split as their parent object, so each one has in this case 25% chance to split. How can I calculate the average number of items, given that the initial chance to split is instead Y, and assuming it can theoretically split forever, and if the splits is also capped to some number N. Maybe format from 1 to N, where N could be infinity?

Question

Andre Ferguson · Accepted Answer

Step 1For this example, we can find the formula by writing out a few terms, we get 1, 1.5, 1.1815.Step 2The terms become   1      /        2    1    ,  1      /        2    2    ,  1      /        2    4    ,  1      /        2          11      , so the formula is   ∑  1      /        2                            n          ⋅          (          n          +          1          )                          2          +          1                      ,  n  =  0 to infinity.

Open question

Answer & Explanation

New Questions in High school geometry