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Question

In the coefficients of (2r+4)th and (r-2)th terms in the expansion of (1=x)18 are equal, find r.


Solution

We know that the coefficient of rth term in the expansion of (1+x)nisnCr1

Coefficient of (2r+4)th term of the expansion (1+x)18=18C2r+41=18C2r+3 and, coefficient of (r-2)th term of the expansion (1+x)18=18Cr21=18Cr3

It is given that these coefficients are equal.

18C2r+3=18Cr3

2r+3=r3 or, 2r+3 +r -3 =18

r =-6 or, 3r =18

[nCr=Csr=s or, r+s=n]

r=6 or, r=6

r=6[ r=-6 is not possible]


Mathematics
RD Sharma
Standard XI

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