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Question

If the interval in which x(>0) must lie so that the greatest term in the expansion of (1+x)100 has the greatest coefficient in (a,b) then 2ab=

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Solution

Greatest coefficient in (1+x)100
= coefficient of middle term = 100C50
Greatest term = 100C50×x50

100C50x50> 100C49x49x>100C49100C50
x>100!49! 51!100!50! 50!x>5051

100C50x50> 100C51x51x<100C50100C51
x<100!50! 50!100!51! 49!x>5051
(a,b)=(5051,5150)
2ab=2×5051×5150=2

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