True/False Question :
Suppose $\left \{ a_{i} \right \}$ is a sequence in $\mathbb{R}$ such that $\sum \left | a_{i} \right |\left | x_{i} \right |< \infty$ whenever $\sum \left | x_{i} \right |< \infty$. Then $\left \{ a_{i} \right \}$ is a bounded sequence.
