Greatest coefficient in (1+x)100
= coefficient of middle term = 100C50
∴ Greatest term = 100C50×x50
100C50x50> 100C49x49⇒x>100C49100C50
⇒x>100!49! 51!100!50! 50!⇒x>5051
100C50x50> 100C51x51⇒x<100C50100C51
⇒x<100!50! 50!100!51! 49!⇒x>5051
∴(a,b)=(5051,5150)
⇒2ab=2×5051×5150=2