1. The problem statement, all variables and given/known data From K=4 to infinity the Σ (-1)^k (k/e^k) Converge or diverge? Use: a) Ratio Test b) Root Test c) Integral Test d) Alternating series test 2. Relevant equations 3. The attempt at a solution For the alternating series test and ratio test I have the correct answer that it converges. These were fairly simple for me to proceed with. However, I am stuck on the Root test and Integral test. For the root test I DID get an answer, but it seems corrupt: Lim as n approaches infinity of (|(-1)^k (k/e^k|))^(1/k) With some simplification I narrowed it down to The lim as n-->infinity of (|n^(1/n)|/e) Which doesn't seem solvable ? And for the Integral test, I am seeing the answer requires imaginary numbers, etc. which we do not use in this class. Is it possible that the instructor did not realize this? Does this problem demand the use of imaginary numbers, etc? If so, I imagine I would be able to pass on this part. Thanks for any guidance.