From 6867a5fa7af1b9e4296c11db9f6cfbd25f424d06 Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 29 Sep 2025 12:50:33 -0600 Subject: [PATCH] vault backup: 2025-09-29 12:50:33 --- education/math/MATH1220 (calc II)/Sequences.md | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 2ca4cd4..91db367 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -69,9 +69,12 @@ $$ \lim_{n \to \infty} \frac{n(n+1)}{2} = \infty $$ Given the above info, the limit is non-zero, so we know that the series diverges. -## Geometric Series +# Geometric Series A geometric series of the form: -$$ \sum_{n = 1}^\inifty ar^{n-1} = \sum_{n=0}^\infty ar^n $$ +$$ \sum_{n = 1}^\infty ar^{n-1} = \sum_{n=0}^\infty ar^n $$ Converges to $\dfrac{a}{1-r}$ if $|r| < 1$ or diverges if $|r| >= 1$. -# E \ No newline at end of file +# Examples: + +> Determine if the series $\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1})$ diverges or converges. If it converges, state where. +