Let \( a_{1}, a_{2}, \ldots \ldots \ldots a_{100} \) be non-zero real numbers such that \( a_{1}...
Let \( a_{1}, a_{2}, \ldots \ldots \ldots a_{100} \) be non-zero real numbers such that \( a_{1} \) \( +a_{2}+\ldots \ldots .+a_{100}=0 \), Then
(a) \( \sum_{i=1}^{100} a_{i} 2^{a_{1}}0 \) and \( \sum_{i=1}^{100} a_{i} 2^{-a_{1}}0 \)
(b) \( \sum_{i=1}^{100} a_{i} 2^{a_{1}} \geq 0 \) and \( \sum_{i=1}^{100} a_{i} 2^{-a_{1}} \geq 0 \)
(c) \( \sum_{i=1}^{100} a_{i} 2^{a_{1}} \leq 0 \) and \( \sum_{i=1}^{100} a_{i} 2^{-a_{1}} \geq 0 \)
(d) sign of \( \sum_{i=1}^{100} a_{i} 2^{a_{1}} \) or \( \sum_{i=1}^{100} a_{i} 2^{-a_{1}} \) depends on the choice of \( a_{i} \) s
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