Geometric means of two summable positive sequences
= Geometric means of two summable positive sequences
The <Cauchy-Schwarz inequality> gives
$$
\sum_n\sqrt{a_nb_n}
\leq\left(\sum_na_n\right)^{1/2}
\left(\sum_nb_n\right)^{1/2}.
$$
= Geometric means of two summable positive sequences
The <Cauchy-Schwarz inequality> gives
$$
\sum_n\sqrt{a_nb_n}
\leq\left(\sum_na_n\right)^{1/2}
\left(\sum_nb_n\right)^{1/2}.
$$