Question #41883

This question tests the student's ability to correctly handle the absolute value function in conjunction with limits and summations.

The primary trap lies in the temptation to commute the summation and the modulus, or to evaluate the sum algebraically before applying the absolute value, which yields the incorrect result of $|-216| = 216$.

Another trap is using a first-order Taylor expansion ($\tan(kx) \approx kx$, $\sin(kx) \approx kx$), which incorrectly evaluates the limit to 0 and leads to the distractor 864.

Because the modulus creates a sign-flipping dependency based on the index $k$, students must first evaluate the standard trigonometric limit for each term, identify the critical transition point ($k=6$), and split the Sigma sum into 'positive' and 'negative' regions before computing the final arithmetic sum.