I am trying to determine: $$\int_\mathbb{R} \sum_{n=1}^\infty \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$$
My idea is that: $$\int_\mathbb{R} \sum_{n=1}^\infty \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$$ $$= \sum_{n=1}^\infty \int_\mathbb{R} \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$$ $$= \sum_{n=1}^\infty \frac{1}{3^n} \cdot 2\cdot2^n$$ $$= 2\cdot \sum_{n=1}^\infty \frac{2^n}{3^n} $$ $$= \frac{2}{1-2/3}-2=6-2=4$$
However a friend of mine is getting 8/3 and we cannot agree on the right result
Any help would be appreciated