# What is the total number of candies can a children get when initially there are $n$?

Assume there are $n$ candies, each candy has a cover, where $2$ candy covers can exchange for a candy. Say if there are 2 candy, then total there will be $2$ candy and $2$ candy cover and in total $3$ candy. Now assume the case when a children has $n$ candy, how many candy can the children get overall? I try to formulate the question but not sure how to get the general formula.

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First count the covers it gets. Say it has $n$ covers, then it can give away 2 and get one new cover. Makes a difference of 1. You stop when you have 1 cover left. So you exchange $n-1$ times. Every time you do an exchange you get a new candy. So you have the original $n$ candies, and the $n-1$ from exchanging, this gives $2n-1$.