Determine if is absolutely convergent, conditionally convergent or divergent.
A) absolutely convergent
B) conditionally convergent
C) divergent

Question

Determine if  is absolutely convergent, conditionally convergent or divergent.
A) absolutely convergent 
B) conditionally convergent 
C) 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