Solution
= Solution
The positive integers below $30$ coprime to $30$ are
$$
1,7,11,13,17,19,23,29.
$$
There are eight, so $\varphi(30)=8$. Their sum can be grouped into four pairs summing to $30$:
$$
\boxed{1+7+11+13+17+19+23+29=120=\frac12\cdot30\cdot8.}
$$
This agrees with the formula.