Use indicator random variables to compute the expected value of the sum of $n$ dice.

Since it is not specified, I must assume the dice in question are 20-sided. Our sample space is $S = \{1, 2, 3, \dots, 20\}$ with $Pr\{1\} = Pr\{2\} = \dots = Pr\{20\} = \frac{1}{20}$. We define our indicator random variable $X_i$ associated with the die showing value $i$.

The expected value of a dice roll is then

$$\begin{split} E[X_k] &= \sum\limits_{i=1}^{20} i \cdot Pr{X_k = i} \\ &= \frac{1 + 2 + \dots + 20}{20} \\ &= \frac{230}{20} \\ &= 11.5 \\ \end{split}$$

Rolling $n$ dice is a collection of $n$ independent events and thus the expected sum is simply $11.5 \cdot n$.