Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

So, this question has two parts... It's not homework, just something I wanted to calculate, but don't know how to for sure.

So, 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. If somebody could explain exactly HOW they get their answer, that would be a lot more useful :). Maybe format from 1 to N, where N could be infinity?

Also, I have no idea what to tag this thing.

share|improve this question
add comment

1 Answer

up vote 0 down vote accepted

I figured out the answer myself.... anyway, for this example, we can find the formula by writing out a few terms, we get 1,1.5,1.1815.

The terms become 1/2^1, 1/2^2, 1/2^4,1/2^11, so the formula is sum 1/2^(n*(n+1)/2+1), n=0 to infinity.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.