Final answer:
The Ratio Test and Root Test both indicate that the series diverges since the terms do not tend towards zero and do not satisfy the criteria of these tests.
Step-by-step explanation:
The student has asked to apply the Ratio Test and Root Test to determine the convergence or divergence of the infinite series ∑k=1[∞]k1. This series is a clear case of divergence because each term k1 grows without bound as k increases, and thus does not satisfy the conditions for convergence under either the Ratio Test or the Root Test. In both tests, the series must have terms that tend towards zero — with the Ratio Test requiring the ratio of successive terms to be less than 1, and the Root Test necessitating the nth root of the nth term also to be less than 1 as n approaches infinity.