From e9aa949b5ef186b33941cd019973f9aaddb09099 Mon Sep 17 00:00:00 2001 From: arc Date: Fri, 3 Oct 2025 11:51:20 -0600 Subject: [PATCH] vault backup: 2025-10-03 11:51:20 --- education/math/MATH1220 (calc II)/Sequences.md | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index a65e179..68d1ba7 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -89,5 +89,8 @@ $$\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1}) = \dfrac{\frac{35}{7}}{1-\frac{2}{7}}$ The divergence test only tells us that if the limit does not equal zero, then the series diverges. If the limit is zero, it doesn't necessarily mean the series converges. -# Eventually converging/diverging -Sometimes a series is not continually positive for the entire series, meaning most tests on series do not apply. To get around this, you can split the series into two or more parts. A finite negative number + infinity is still infinity, and a finite negative number + a finite number is still a finite number. \ No newline at end of file +# Alternating series test +Sometimes a series is not continually positive for the entire series, meaning most tests on series do not apply. To get around this, you can split the series into two or more parts. A finite negative number + infinity is still infinity, and a finite negative number + a finite number is still a finite number. + +A simple example of an alternating series is: +$$ \sum_{n=1}^\infty (-1)^{n+1}a_n = a_1 - a_2 + a_3 - a_4 $$ \ No newline at end of file