$$f(x)=\frac{1}{2^{n-1}} \quad if \quad 1/2^n<x\leq 1/2^{n-1}$$ $x$ belongs to $[0,1]$, n belongs to natural numbers and $f(0)=0$. Find the value of the integral of $f(x)$ from 0 to 1.
If I put $n=1$ I get the interval $1/2<x\leq 1$ and for other values of $n$ I get smaller and smaller intervals. Event though I am able to get a slight picture here I am having difficulty in proceeding further. I would like some hints on how to approach this problem.
A hint: $$ \int_{0}^{1} f = \sum_{n=1}^{\infty} \int_{\frac{1}{2^n}}^{\frac{1}{2^{n-1}}} f $$