First slide

Binomial theorem for positive integral Index

Question

The sum of the coefficient in the expansion of ${(1 + ax - 2 x^{2})}^{n}$ is

Moderate

A

positive, when $a < 1 and n = 2 k, k \in N$
B

negative, when $a < 1 and n = 2 k + 1, k \in N$
C

positive, when $a > 1 and n \in N$
D

zero, when a = 1

Solution

We know that to get the sum of coefficients, we put x = 1.
Then, sum of coefficients is ${(1 + ax - 2 x^{2})}^{n} is (a - 1)^{n}$
Obviously, when a > 1, sum is positive for any n.

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