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in expansion of [3^1/7+5^1/49]^4319,THE NUMBER OF TERMS FREE FROM RADICALS IS.....??

in expansion of [3^1/7+5^1/49]^4319,THE NUMBER OF TERMS FREE FROM RADICALS IS.....??

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hello Student,
The general term in the expansion of[3^1/7+5^1/49]^4319 is nCr (x)^(n-r).a^r
=4319Cr(3^1/7)^(4319-r).(5^1/49)^r
=4319Cr.3^(4319-r)/7. (5)^r/49
=4319Cr (3)^(617-r/7).(5)^r/49
This term will be free of radical if r is multiple of 49 .But r<n so value of r may be 49,98,147,.............
If we divide 4319 by 49 we get 88 as quotient. It means there will be 88 term which will be free of radicals.
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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