where are real numbers.
Now I want to prove with the intermediate value theorem that this equation has solutions in the real numbers.
With , you can see that every summand gets smaller than the summand before.
My other thought was that about the -summands, with the intermediate value theorem you know that every zero (point) is in the interval and is located between the -summands. So there are solutions for this equation!
How can I prove my thoughts in a formal correct way? (Are my thoughts generally correct?)