Question

Discuss the convergence of the harmonic series $\sum _{n=1}^{\infty }\frac{1}{n}$

Answer 1

Given,

${\sum }_{n=1}^{\infty }\frac{1}{n}$

$\sum a_n$ converges, if and only if,

For every $ϵ>0$ there is a natural number N such that, $|a_{n+1}+a_{n+2}+\dots +a_{n+p}|<ϵ,\forall n>N$ and $p\ge 1$

$=diverges$