Determine if is absolutely convergent, conditionally convergent or divergent.

Question

Determine if  is absolutely convergent, conditionally convergent or divergent.

Quizplus · Accepted Answer

To determine convergence, we need to analyze the limit of the absolute value of the given series. 
|11eaa88b| + |90e8| + |8730| + |a696| + |13d2ca97c720| + |TB5869| + |11| = primarily depends on the length of the numbers in each term. Thus, the series is comparable to $\sum_{n=1}^\infty \frac{1}{n^p}$ where $p$ is the length of the numbers (number of digits). It is known that the $p$-series is convergent if and only if $p>1$. Since every term in the given series has a length greater than 1, the series converges absolutely by the comparison test.

Determine If Is Absolutely Convergent, Conditionally Convergent or Divergent