Question

Evaluate: $$ \lim_{n \to \infty} \frac{1}{n^{k+1}} \left[ 2^k + 4^k + 6^k + \dots + (2n)^k \right]. $$ 

• A. \( \frac{2^k}{k} \)
• B. \( \frac{2^{k+1}}{k+1} \)
• C. \( \frac{2^k}{k+1} \)
• D. \( \frac{2^k}{k-1} \)