Evaluate the sum $\sum_{k=1}^{11}(-13 k)$

Step 1 ：The sum \(\sum_{k=1}^{11}(-13 k)\) is an arithmetic series with first term -13 and common difference -13.

Step 2 ：The sum of an arithmetic series can be calculated using the formula \(\frac{n}{2}(a + l)\) where n is the number of terms, a is the first term, and l is the last term.

Step 3 ：In this case, n = 11, a = -13, and l = -13*11 = -143.

Step 4 ：Substituting these values into the formula, we get the sum = \(\frac{11}{2}(-13 - 143) = -858\).

Step 5 ：Final Answer: The sum of the series is \(\boxed{-858}\).