Determine whether the series converges absolutely,converges conditionally,or diverges.
A)converges absolutely
B)diverges
C)converges conditionally

Question

Determine whether the series  converges absolutely,converges conditionally,or diverges. ​
A)converges absolutely 
B)diverges 
C)converges conditionally

Quizplus · Accepted Answer

Since the series contains only positive terms (11, eac44f_ec3b_e552_bedf_9306fe30f93d_TB7497_11), it is not necessary to check for conditional convergence. We can instead focus on absolute convergence. One way to do this is to use the Comparison Test, where we compare the series to a geometric series with a common ratio of 1/2. This series converges (since |1/2| < 1), so the given series also converges absolutely by the Comparison Test.

Determine Whether the Series Converges Absolutely,converges Conditionally,or Diverges