You roll a fair six-sided die repeatedly and keep a running total of the results. The moment you roll a $1$, you stop -- and that $1$ is **not** added to your sum. What is the expected value of your final sum?

Expected Sum Until Rolling a 1

Expectation · Medium · Free problem

You roll a fair six-sided die repeatedly and keep a running total of the results. The moment you roll a

$, you stop -- and that

$ is **not** added to your sum. What is the expected value of your final sum?