Determine whether the series [infinity] ln(2n) 3n n=1 converges or diverges. SOLUTION The function f(x) = ln(2x) (3x) is positive and continuous for x > because the logarithm function is continuous. But it is not obvious whether or not f is decreasing, so we compute its derivative: f '(x) = 3x − 3 ln(2x) 9x2 = 3x2 .