If n is not a multiple of 3, then the coefficient of `x^n` in the expansion of `log_e (1+x+x^2)`is : (A) `1/n` (B) `2/n` (C) `-1/n` (D) `-2/n`

Options

A. `(-2)/(n)`
B. `(2)/(n)`
C. `(1)/(n)`
D. none of these

Explanation

To find the coefficient of \( x^n \) in the expansion of \( \log_e(1 + x + x^2) \) when \( n \) is not a multiple of 3, we can follow these steps:

### Step 1: Rewrite the logarithm
We start with the expression:
\[ \log_e(1 + x + x^2) \]
We can factor this expression:
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