can't figure out display math

src/10_xray_solutions.md

@@ -148,24 +148,24 @@ $S(\mathbf{G}) = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi
 
 Solving for $h$, $k$, and $l$ results in 
 
-$$
+$
 S(\mathbf{G}) = \begin{cases}
     2f, \: \text{if $h+k+l$ is even}\\
     0, \: \text{if $h+k+l$ is odd}.
 \end{cases}
-$$
+$
 Thus if $h+k+l$ is odd, diffraction peaks dissapear
 
 3.
 
 Let $f_1 \neq f_2$, then
 
-$$
+$
 S(\mathbf{G}) = \begin{cases}
 f_1 + f_2, \text{if $h+k+l$ is even}\\
 f_1 - f_2, \text{if $h+k+l$ is odd}
 \end{cases}       
-$$
+$
 
 4.
 Due to bcc systematic absences, the peaks from lowest to largest angle are: