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 expansion (x +y)n is given by,
Now, finding the (r – 5)th term, we get
Tr-5 = 34Cr-6 x xr-6
Thus, the coefficient of (r – 5)th term is 34Cr-6
Now, finding the (2r – 1)th term, we get
T2r-1 = 34C2r-2 x (x)2r-2
Thus, coefficient of (2r – 1)th term is 34C2r-2
As the coefficients are equal, we get
34C2r-2 = 34Cr-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