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Which is larger : (99^(50)+100^(50)) or ...

Which is larger : `(99^(50)+100^(50))` or `(101)^(50)`.

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To determine which is larger between \(99^{50} + 100^{50}\) and \(101^{50}\), we can use the Binomial Theorem to expand \(101^{50}\) and \(99^{50}\). ### Step 1: Expand \(101^{50}\) Using the Binomial Theorem, we can express \(101^{50}\) as: \[ 101^{50} = (100 + 1)^{50} = \sum_{k=0}^{50} \binom{50}{k} 100^{50-k} \cdot 1^k \] This expansion gives us: ...
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