If the coefficients of (r – 5)th and (2r – 1)th terms in the expansion of (1 + x)34 are equal, find the value of r.

To find: the value of r with respect to the binomial expansion of (1 + x)34 where the coefficients of the (r – 5)th and (2r – 1)th terms are equal to each other


Formula Used:


The general term, Tr+1 of binomial expansionis given by,


Tr+1 nCr xn-r yr where


nCr


Now, finding the (r – 5)th term, we get


Tr-534Cr-6


Thus, the coefficient of (r – 5)th term is 34Cr-6


Now, finding the (2r – 1)th term, we get


T2r-134C2r-2


Thus, coefficient of (2r – 1)th term is 34C2r-2


As the coefficients are equal, we get


34C2r-234Cr-6


2r-2=r-6


r=-4


Value of r=-4 is not possible


2r-2+r-6=34


3r=42


r=14


Thus, value of r is 14


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