I am studying real analysis and find something difficult to understand.
THM. Given monotone increasing function $f_{n}:[a,b]\to \Bbb R$, $(n=1, 2, \ldots)$, put
$$
s_{n}=\sum_{k=1}^n f_{k}.
$$
If $s_{n}$ converges pointwise to $s$, then
$$
s'=\sum_{n_=1}^\infty (f_{n})'.
$$
At first I want to understand why $$ \sum_{n=1}^\infty (f_{n})'\le s' $$ Please help or give me some hint. Thanks.