Question

I know for a fact that harmonic series diverge. But what about harmonic sequences?

If you take the limit of the harmonic sequence, it equals "0" which means that it converges right?

Answer 1

It is true that the harmonic series diverges, and the sequence converges. But if you are asking the question:\[\sum_{i=0}^\infty a_n\]does the series converge, it is not enough to check that:\[\lim_{n\longrightarrow \infty}a_n=0\]The harmonic series is an example of that.

Answer 2

THANK YOU! Your first sentence answered my question!