Solution
= Solution
For positive $a_n,b_n$,
$$
\sqrt{a_n^2+b_n^2}\leq a_n+b_n.
$$
The <comparison test for series> therefore gives
$$
\boxed{\sum_n\sqrt{a_n^2+b_n^2}
\leq\sum_na_n+\sum_nb_n<\infty.}
$$
= Solution
For positive $a_n,b_n$,
$$
\sqrt{a_n^2+b_n^2}\leq a_n+b_n.
$$
The <comparison test for series> therefore gives
$$
\boxed{\sum_n\sqrt{a_n^2+b_n^2}
\leq\sum_na_n+\sum_nb_n<\infty.}
$$