Expected minimum of three 100-sided dice

Three fair dice, each numbered $1$ to $100$, are rolled. What is the expected value of the smallest number showing?

$25.5025$. Sum the tail probabilities: $\mathbb{P}(\min\ge k)=\left(\tfrac{101-k}{100}\right)^3$, so the expectation is $\tfrac{1}{100^3}\sum_{j=1}^{100}j^3=\tfrac{5050^2}{10^6}=25.5025$.