$\sum\_{n\in S}$$\frac{1}{n}$, where S consists of those positive integers whose decimal expansion does not contain the digit 1.

This was a part(b) question. 

Part (a) was an evaluation of the double integral $\int \int\_S$ $(x^2 + y^2)d\sigma$, where S is the unit sphere centered at (0,0,0), and $\sigma$ is surface area. The answer is $\frac{8\pi}{3}$.

I don't see how part(a) can be used to solve part(b). 

For the series evaluation, if we are summing over the positive integers that don't contain the digit 1, then I'm thinking we exclude integers such as 1, which has decimal expansion .99999.. or 1.0000, or 10, which has expansion 9.9999... or 10.0000, etc, and we sum over numbers such as 2, 3, 4, 5, ... 

Not sure where I can go with this idea, though.

Thanks,