diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 0b4a6f8..6fbc43a 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/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: +$$ \sum_{n=1}^\infty \frac{1}{2^n} = \lim_{n \to \infty}S_n = \lim_{n \to \infty} (1 - \frac{}{}$$ \ No newline at end of file