Question 18 (1 point) Evaluate sum _(i=1)^n(i+1)= (n^2+2n)/(2) (n^2+n)/(2) (n^2+3n)/(2) (n^2+3)/(2) infty

## Step 1: Separate the Summation<br />### We can separate the summation into two parts: $\sum_{i=1}^{n} (i+1) = \sum_{i=1}^{n} i + \sum_{i=1}^{n} 1$.<br /><br />## Step 2: Evaluate the Summations<br />### We know that $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$ and $\sum_{i=1}^{n} 1 = n$. Therefore, $\sum_{i=1}^{n} (i+1) = \frac{n(n+1)}{2} + n$.<br /><br />## Step 3: Simplify the Expression<br />### Simplify the expression by finding a common denominator: $\frac{n(n+1)}{2} + \frac{2n}{2} = \frac{n^2 + n + 2n}{2} = \frac{n^2 + 3n}{2}$.