If `A_r=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|,` the value of `sum_(r=1)^n A_r` is (A) `n` (B) `2n` (C) `-2n` (D) `n^2`

Explanation

To solve the problem, we need to evaluate the determinant \( A_r \) and then find the sum \( \sum_{r=1}^{n} A_r \).

### Step 1: Write down the determinant \( A_r \)

The determinant is given as:

\[
A_r = \begin{vmatrix}
...