I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
You're thinking of a different calculus problem in this case we are comparing the growth rate of 100*\infty vs \infty. In calculus, you cannot accelerate the growth of \infty. If you put \infty / \infty your answer will be undefined (you can double check with Wolfram), similarly, if you put 100*\infty / \infty, you will also get undefined