Sum the following geometric series to infinity: `(sqrt(2)+1)+1+(sqrt(2)-1)+oo` `1/2+1/(3^3)+1/(2^3)+1/(3^4)+1/(2^5)+1/(3^6)+oo`

Explanation

To solve the given geometric series to infinity, we will break it down into two parts as described in the question.

### Part 1: Sum of the Series `(sqrt(2)+1) + 1 + (sqrt(2)-1) + ...`

1. **Identify the first term (a) and the common ratio (r)**:
- The first term \( a = \sqrt{2} + 1 \).
- The next term is \( 1 \).
- The third term is \( \sqrt{2} - 1 \).
...