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Question

The number of rational terms in the expansion of the (719+13111)1980 is

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Solution

The general term of the expansion of the (719+13111)1980 is given by Tr+1= 1980Cr (719)1980r (13111)rTr+1= 1980Cr (7)220 (7)r9 (13)r11
So, for the rational terms r must be multiple of both 9 & 11. In other words, r must be multiple of 99.
r=0,99,198,....,1980, total 21 terms

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