Question 1:
The thirteenth century French polymath Nicolas Oresme proved that the harmonic series does not converge. Prove this result.
Question 2:
Prove that does not converge.
Question 3:
Prove that does not converge.
Even if you solve these all on your own, you won’t achieve the glory of that French polymath, but you will have “re-discovered” some “elements of truth of analysis” …You can give yourself a pat on the back!
Cheers,
Nalin Pithwa.