convergent series, sequences? I want to construct a sequence of rational numbers whose sum converges to an irrational number and whose sum of absolute values converges to 1.
I can find/construct plenty of examples that has one or the other property, but I am having trouble find/construct one that has both these properties.
Any hints(not solutions)? 

Find two irrational numbers $a > 0$ and $b < 0$ such that $a-b = 1$ but $a+b$ is irrational. Create a series with positive terms that sum to $a$ and another series with negative terms that sum to $b$. Combine the two series.
