Determine whether the following series is an absolute convergence, conditional convergence, or divergent and by what test: ā,ā,n=1 ((-1)^{n}ln(n))/(2.5)^{n}
Determine whether the following series is an absolute convergence, conditional convergence, or divergent
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1 Answer
Use the ratio test:
lim_{nāā}((ln(n+1)/2.5^{n+1})/(ln(n)/2.5^{n}) = lim ((ln(n+1)/ln(n))/2.5) = 1/2.5 <1
Therefore, the series converges absolutely.