Update Unit 2: Sequences, Series, and Financial Applications.md

Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md

@@ -88,4 +88,26 @@ for(int i=1; i<=N; i++) {
 
 Either the series **converges** and **diverges**. There is only a finite sum when the series **converges**.
 
-Recall the 
+Recall the our formula is $`\dfrac{a(r^n-1)}{r-1}`$, and is $`n`$ approaches $`\infty`$, if $`r`$ is less than $`1`$, then $`r^n`$ approaches $`0`$. So this
+series converges. Otherwise, $`r^n`$ goes to $`\infty`$, so the series diverges.
+
+If the series diverges, then the sum can be calculated by the following formula:
+
+If $`r = \dfrac{1}{2}`$, then $`\large \lim_{x \to \infty} (\frac{1}{2})^x = 0`$ Therefore, $`S_n = \dfrac{a(1 - 0)}{1 - r}`$. This works for any $`|r| \lt 1`$
+
+## Binomial Expansion
+A binomial is a polynomial expression with 2 terms.
+
+A binomial expansion takes the form of $`(x + y)^n`$, where $`n`$ is an integer and $`x, y`$ can be any number we want.
+
+A common relationship of binomial expansion is pascal's triangle. The $`nth`$ row of the triangle correspond to the coefficent of $`(x + y)^n`$
+
+```
+            1           row 0
+           1 1          row 1
+          1 2 1         row 2
+         1 3 3 1        row 3
+        1 4 6 4 1       row 4
+      1 5 10 10 5 1     row 5        
+```
+