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Question

If in the expansion of (1+x)20, the coefficients of rth and (r+4)th terms are equal, then r is equal to?

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Solution

We are given In the expansion of (1+x)20, the coefficients of rth and (r+4)th terms are equal.
here the any rth term will be
Tr=(nr1)(a)nr+1(b)r1
now, here a=1 & b=x
so, the coefficient of rth term is =(nr1)(1)nr+1,n=20
=(20r1)
& the co-efficient of (r+4)th term is =(nr+41)(1)nr4+1,n=20
=(20r+3)
so, (20r1)=(20r+3)
now, it (nr1)=(nr2) n=r1+r2
so, 20=r1+r+3
2r+2=20
2r=18
r=9
The r is equal to 9

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