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education/math/MATH1220 (calc II)/Sequences.md

@@ -65,3 +65,13 @@ $$ \sum_{n=1}^\infty \frac{1}{2^n} = \lim_{n \to \infty}S_n = \lim_{n \to \infty
 - $S_2 = 1 + 2 = 3$
 - $S_n = \frac{n(n+1)}{2}$ 
 So: 
+$$ \lim_{n \to \infty} \frac{n(n+1)}{2} = \infty $$
+
+Given the above info, the limit is non-zero, so we know that the series diverges.
+
+## Geometric Series
+A geometric series of the form:
+$$ \sum_{n = 1}^\inifty ar^{n-1} = \sum_{n=0}^\infty ar^n $$
+Converges to $\dfrac{a}{1-r}$  if $|r| < 1$ or diverges if $|r| >= 1$. 
+
+# E