I looked a lot on the internet for examples and I tried to do it myself, but I haven't seen any infinite sums of rational numbers that equal for example something like square root of 10 or cube root of 2.
The famous ones that I've seen end up adding to integers or a fraction of pi, but I haven't seen any irrational numbers that aren't transcendental.
Is there a method where I can pick an irrational number and then make an infinite sum using rational numbers where they are equal?
like the continued fraction for square root of 10 is 3.666666666... can I use that somehow to make an expression for the infinite sum using rational numbers? What about if it goes to a cube root?
I'd also really like it if someone could make my question a little clearer using the right math words and such, I really did my best to describe it.