I'm looking to answer the following question:
There are given two increasing sequences $$a_n : 0.001; 0.004; 0.009; ... $$ $$b_n : 100; 300; 500; ... $$
Can the 1st sequence catch up with the 2nd(that is, can the inequality $a_n > b_n$ be satisfied for some $n$)
Looking at the 2 sequences I suspect that $a_n$ will surpass $b_n$ for some n as the intervals for a_n are growing.
How would I describe the situation in mathematical notation? In other words, I can see the answer to the question but I don't know how to write it down mathematically.