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TIFR-2013-Maths-B: 16

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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.

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