Question

Prove rigorously that an infinite sum of rationals can yield an irrational.

Answer 1

I know how to do a case-by-case proof, but I'd like to see one that is true for all cases where an infinite sum of rationals yield an irrational.

Answer 2

"can" means you only need one example. so there would be no "general" way to do it because it is not true in general

Answer 3

You're right. I should have said "demonstrate rigorously the conditions under which an infinite sum of rationals will yield an irrational".