In the binomial expansion of (a + b)n, the coefficients of the 4th and 13th terms are equal to each other. Find the value of n.

To find: the value of n with respect to the binomial expansion of (a + b)n where the coefficients of the 4th and 13th terms are equal to each other


Formula Used:


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


Tr+1 nCr xn-r yr where


nCr


Now, finding the 4th term, we get


T4nC3


Thus, the coefficient of a 4th term is nC3


Now, finding the 13th term, we get


T13nC12


Thus, coefficient of 4th term is nC12


As the coefficients are equal, we get


nC12= nC3


Also, nCr= nCn-r


nCn-12=nC3


n-12=3


n=15


Thus, value of n is 15


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