Question

If the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

The given expression is `(x - 1/x^2)^(2n)` 

T_r+1 = `""^(2n)C_r (x)^(2n - r) (- 1/x^2)^r`

= `""^(2n)C_r (x)^(2n - r) (-1)^r * 1/x^(2r)`

= `""^(2n)C_r (x)^(2n - r - 2r) (-1)^r`

= `""^(2n)C_r (x)^(2n - 3r) (-1)^r`

For the term independent of x, 2n – 3r = 0

∴ r = `(2n)/3` which not an integer and the expression is not possible to be true