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

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

Text Solution

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Consider, ` (101)^(50) - (99)^(50) - (100)^(50)`
`= {(100)^(50)(1+0.01)^(50)-(1-0.01)^(50)-1)}`
`= (100)^(50){2.[C_(1)(0.001)+^(50)C_(3)(0.01)^(3)+...]-1}`
` = (100)^(50){2[^(50)C_(3)(0.01)^(3)+^(50)C_(5) (0.01)^(5) +…]}`
` ( 101)^(50) - {(99)^(50) + (100)^(50)}gt 0`
` (101)^(50) gt (99)^(50) + ( 100) ^(50)`
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