diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index b722240..2ca4cd4 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -64,4 +64,14 @@ $$ \sum_{n=1}^\infty \frac{1}{2^n} = \lim_{n \to \infty}S_n = \lim_{n \to \infty - $S_1 = 1$ - $S_2 = 1 + 2 = 3$ - $S_n = \frac{n(n+1)}{2}$ -So: \ No newline at end of file +So: +$$ \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 \ No newline at end of file