>>12680646The only reason I could think of for you struggling with the proof is because you don't have a strong understanding of what an infinite series is--or what infinity means. I'm not trying to patronize you but literally watch the Ted Talk on Hilbert's Hotel and see if that helps. The proof is really very simple: the harmonic series is bigger than this other series that diverges, and therefore it diverges:
(the inequality is true because both exponentiation and the ceiling function are strictly increasing and in the denominator).
Which is nothing but 1 + 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 …
Combining terms gives 1 + 1/2 + 1/2 + 1/2 which clearly diverges.
