Binomial TheoremHard
Question
If n is even natural and coefficient of xr in the expansion of 
is 2n, (|x| < 1), then -
is 2n, (|x| < 1), then - Options
A.r ≤ n/2
B.r ≥ (n - 2)/2
C.r ≤ (n + 2)/2
D.r ≥ n
Solution
y = (1 - x)-1 (1 + x)n
y = (1 + x + x2 +... ∞) (1 + x)n
y = (1 + x)n + x(1 + x)n + x2 (1 + x)n + ....
Co-efficient of xr =
nCr + nCr-1 + .... nC0 = 2n
r ≥ n (As nCn+1) = 0
y = (1 + x + x2 +... ∞) (1 + x)n
y = (1 + x)n + x(1 + x)n + x2 (1 + x)n + ....
Co-efficient of xr =
nCr + nCr-1 + .... nC0 = 2n
r ≥ n (As nCn+1) = 0
Create a free account to view solution
View Solution FreeMore Binomial Theorem Questions
The sum of coefficients of odd powers of x in the expansion of (1 + x)n is -...The co-efficient the middle term in the expansion of ( 1 + x)2n is -...The sum of the binomial coefficients of is equal to 256. The constant term in the expansion is -...If the coefficient of third term in the expansion of is 27 more than the coefficient of second term, then the value of n...f C0,C1, C2, ....Cn are binomial coefficients of different terms in the expansion of (1 + x)n then C0 − 2.C1 + 3.C...