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
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