Determine whether the following series is an absolute convergence, conditional convergence, or divergent

Question

Determine whether the following series is an absolute convergence, conditional convergence, or divergent and by what test: ∑,∞,n=1  ((-1)ⁿln(n))/(2.5)ⁿ

Answer 1

Use the ratio test:

 

lim_n→∞((ln(n+1)/2.5ⁿ⁺¹)/(ln(n)/2.5ⁿ) = lim ((ln(n+1)/ln(n))/2.5) = 1/2.5 <1

 

Therefore, the series converges absolutely.