Let us have a sequence $a_n$ of positive rational numbers, for which $sum a_n = R in mathbb R$. Now suppose $b_n$ is a subsequence of $a_n$ such that $sum b_n = r < R$. The question is "Can ...

Let us have a sequence $a_n$ of positive rational numbers, for which $sum a_n = R in mathbb R$. Now suppose $b_n$ is a subsequence of $a_n$ such that $sum b_n = r < R$. The question is "Can ...