The problem is to evaluate the sum $\sum_{i=4}^{30} 4i$.

1. Problem Description

The problem is to evaluate the sum $\sum_{i=4}^{30} 4i$.

2. Solution Steps

The summation $\sum_{i=4}^{30} 4i$ can be rewritten as $4 \sum_{i=4}^{30} i$.

We can use the formula for the sum of the first $n$ integers:

$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$

We can express $\sum_{i=4}^{30} i$ as $\sum_{i=1}^{30} i - \sum_{i=1}^{3} i$.

Using the formula, $\sum_{i=1}^{30} i = \frac{30(30+1)}{2} = \frac{30(31)}{2} = 15(31) = 465$.

And $\sum_{i=1}^{3} i = \frac{3(3+1)}{2} = \frac{3(4)}{2} = 6$.

Therefore, $\sum_{i=4}^{30} i = 465 - 6 = 459$.

Finally, $\sum_{i=4}^{30} 4i = 4 \sum_{i=4}^{30} i = 4(459) = 1836$.

3. Final Answer

1836