Let $\displaystyle \mu $ be a measure on the set of natural numbers.

And define $\displaystyle \mu ( \{ n, n+1, ... \} ) = \frac {n}{2^n} $ for $\displaystyle n = \{ 1, 2, 3, ... \} $

Find $\displaystyle \int x d \mu (x) $

My solution so far:

To be honest I'm a bit lost in this one. So should I have something like $\displaystyle \sum ^ \infty _{x=1}\frac {x}{2^x } $?