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

@@ -52,3 +52,10 @@ Given the above series, we can define the following:
 and say that the sum converges to $L$. 
 
 ## Examples
+> Prove that $\sum_{n = 1}^\infty a_n = L$
+- $S_1 = \frac{1}{2}$
+- $S_2 = \frac{1}{2} + \frac{1}{4} = \frac{3}{4}$ 
+- $S_3 = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} = \frac{7}{8}$ 
+- $S_n = \frac{2^n - 1}{2^n}$
+So:
+$$ \sum_{n=1}^\infty \frac{1}{2^n} = \lim_{n \to \infty}S_n = \lim_{n \to \infty} (1 - \frac{}{}$$