Can all algebraic numbers (i.e. quantities such as $3/5$, $\sqrt{2}$, $\sqrt{3}$, etc.) be expressed as an infinite sum whose summands never permanently vanish?
A well known example is $\sum_{n=1}^\infty\frac{1}{2^n}=1.$
I realise we could always multiple this infinite summation by any number we like, but what if this were not permitted?