Ratio/Interval of Convergence

Question

What is the ratio of convergence and interval of convergence of f in a power series like:

f(x) = (x^(2) / 5^(2)ln2) - (x^(3) / 5^(3)ln3) + (x^(4) / 5^(4)ln4) - (x^(5) / 5^(5)ln5) + ...

Answer 1

The general term appears to be xⁿ⁺¹/(5ⁿ⁺¹ln (n+1))

The ratio of the n+2 term to the n+1 term converges to x/5 (and you should prove that!).

With that information you should be able to answer the question.