question 3 (1 point) a series ∑n=1∞an exhibits absolute convergence if ∑n=1∞|an| converges. diverges…

question 3 (1 point) a series ∑n=1∞an exhibits absolute convergence if ∑n=1∞|an| converges. diverges. question 4 (1 point) a series ∑n=1∞an exhibits conditional convergence if ∑n=1∞an converges but ∑n=1∞|an| converges. diverges.

question 3 (1 point) a series ∑n=1∞an exhibits absolute convergence if ∑n=1∞|an| converges. diverges. question 4 (1 point) a series ∑n=1∞an exhibits conditional convergence if ∑n=1∞an converges but ∑n=1∞|an| converges. diverges.

Answer

Brief Explanations:

  1. For Question 3: By the definition of absolute - convergence of a series $\sum_{n = 1}^{\infty}a_n$, it converges absolutely if the series of absolute values $\sum_{n=1}^{\infty}|a_n|$ converges.
  2. For Question 4: By the definition of conditional - convergence of a series $\sum_{n = 1}^{\infty}a_n$, it converges conditionally if $\sum_{n = 1}^{\infty}a_n$ converges but $\sum_{n=1}^{\infty}|a_n|$ diverges.

Answer:

Question 3: converges. Question 4: diverges.