The value of `lim_(n->oo){(1+2+3++n)/(n+2)-n/2}\ ` is a. 1 b . -1 c. 1/2 d. -1/2

Explanation

To solve the limit problem \( \lim_{n \to \infty} \left( \frac{1 + 2 + 3 + \ldots + n}{n + 2} - \frac{n}{2} \right) \), we will follow these steps:

### Step 1: Use the formula for the sum of the first n natural numbers
The sum of the first n natural numbers is given by the formula:
\[ S_n = \frac{n(n + 1)}{2} \]
Thus, we can rewrite the limit as:
...