question 2 (2 points)\nwhat conditions must a series have in order to use the alternating series test for…

question 2 (2 points)\nwhat conditions must a series have in order to use the alternating series test for convergence?\nlim bn = l, l ≠ 0\nbn→∞\n0 < bn+1 ≤ bn for all n ≥ 1\nlim bn = 0\nbn→∞\nit is an alternating series.

question 2 (2 points)\nwhat conditions must a series have in order to use the alternating series test for convergence?\nlim bn = l, l ≠ 0\nbn→∞\n0 < bn+1 ≤ bn for all n ≥ 1\nlim bn = 0\nbn→∞\nit is an alternating series.

Answer

Brief Explanations:

The alternating - series test for convergence applies to an alternating series $\sum_{n = 1}^{\infty}(-1)^{n - 1}b_n$ or $\sum_{n = 1}^{\infty}(-1)^{n}b_n$ where $b_n>0$. The conditions are: the series must be alternating, $0 < b_{n + 1}\leq b_n$ for all $n\geq1$ (the terms are non - increasing in magnitude), and $\lim_{n\rightarrow\infty}b_n = 0$.

Answer:

B. $0 < b_{n+1} \leq b_{n}$ for all $n \geq 1$ C. $\lim_{b_{n}\to\infty}b_{n}=0$ D. It is an alternating series.