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

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

Use the ratio test:
 
limnā†’āˆž((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.