Question

a series is convergent iff its corresponding sequence is convergent????? is this true

Answer 1

I give you a counterexample of this
sequence \[\sum_{n=1}^{\infty}\frac{ 1 }{ n }= \frac{ 1 }{ 1 }+\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 }+......=infty\]
but \[\lim_{n \rightarrow \infty}\frac{ 1 }{ n }=0\]
what does it mean?
It means the corresponding sequence is diverge but the series is converge