Thread: 1 + 1/2 + 1/3 + ...

Hi I need hints on any of these questions. I wasn’t able to express the series as a geometric sum or anything I could work with:

1. Prove that 1+1/2+1/3+...+1/1000<10

2. Prove that 1 + 1/2 + 1/3 + 1/4 + ... equals infinity

Originally Posted by Aquafina

Hi I need hints on any of these questions. I wasn’t able to express the series as a geometric sum or anything I could work with:

1. Prove that 1+1/2+1/3+...+1/1000<10

2. Prove that 1 + 1/2 + 1/3 + 1/4 + ... equals infinity

One question per thread please.

#2)Use the Integral Test.