InterviewSolution
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InterviewSolution
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Which is larger : `(99^(50)+100^(50))` or `(101)^(50)`.A. `99^(50) + 100^(50)`B. both are equalC. ` (101)^(50)`D. none of these |
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Answer» Correct Answer - c We have , ` 99^(50) + 100 ^(50) - 101^(50)` ` = (100 - 1 )^(50) - (1 - 100)^(50) + 1000^(50)` ` = - {(1 +100)^(50) - (1 - 100)^(50)} + 100^(50)` ` = - 2 {""^(50)C_(1)xx100 +""^(50)C_(3)xx100^(3) + ... + ""^(50)C_(49)xx100^(49)} + 100^(50)` ` = - 2 {""^(50)C_(1)xx100 +""^(50)C_(3)xx100^(3) + ... + ""^(50)C_(47)xx100^(49)} lt 0` ` therefore 99^(50) + 100^(50) - 101 ^(50) lt 0 rArr 00^(50) + 100^(50) lt 101^(50)`. |
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