Squares of a summable positive sequence
= Squares of a summable positive sequence
If $a_n\geq0$ and $\sum a_n<\infty$, then $a_n\to0$, so eventually $a_n^2\leq a_n$ and $\sum a_n^2$ converges.
= Squares of a summable positive sequence
If $a_n\geq0$ and $\sum a_n<\infty$, then $a_n\to0$, so eventually $a_n^2\leq a_n$ and $\sum a_n^2$ converges.