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