vault backup: 2025-09-29 12:50:33

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
+# Examples:
+
+> Determine if the series $\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1})$ diverges or converges. If it converges, state where.
+