(2) A series is said to be “alternating" if the signs of subsequent terms switch between positive and negative. Typically, alternating series have a factor of (–1)" to make the signs switch between terms. (a) To further explore this idea, write out the first six terms of the following series: (-1)" n! (b) Now, use the ratio test to determine if this series converges:
(2) A series is said to be “alternating” if the signs of subsequent terms switch between positive
and negative. Typically, alternating series have a factor of (−1)nto make the signs switch
between terms.
(a) To further explore this idea, write out the first six terms of the following series:
∞∑
n=0
(−1)n
n! =
(b) Now, use the ratio test to determine if this series converges:
(c) For this question, navigate to the Wolfram Alpha website (wolframalpha.com)
and type the series from part (a) into the search bar. You should be able to use
written words like, “The sum from n=0 to infinity of...” (this is the method I typically
use), or you can type some math text such as sum_(n=0)^infinity to refer to the sum.
What do you notice about the results you get?
*Pease write a detail as much as possible
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