Question

What is the sign of the second term of the expansion of (x - y)^n for n = 3, 4, and 5?

Answer 1

Answer:

Correct choice is B

Step-by-step explanation:

The i-th term of the binomial expansion $\left(x-y\right)^{n}$ is

$T_i=C^{n}_{i-1}\cdot \left(x\right)^{n+1-i}\cdot (-y)^{i-1}.$

For any n, when i=2,

$T_2=C^{n}_{2-1}\cdot x^{n+1-2}\cdot (-y)^{2-1}=-C^{n}_1\cdot x^{n-1}\cdot y.$

Since $C^{n}_1$ is always positive, then the second term has negative sign.