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