diff --git a/notes/剑指 offer 题解.md b/notes/剑指 offer 题解.md
index cc82b048..6e54a559 100644
--- a/notes/剑指 offer 题解.md	
+++ b/notes/剑指 offer 题解.md	
@@ -600,35 +600,41 @@ public int JumpFloorII(int target) {
 }
 ```
 
-### 数学式子推导
+### 数学推导
+
+跳上 n-1 级台阶，可以从 n-2 级跳 1 级上去，也可以从 n-3 级跳 2 级上去...，那么
 
-跳上 n-1 级台阶，可以从 n-2 级跳 1 级上去，也可以从 n-3 级跳 2 级上去...也可以从 0 级跳上去。那么
 ```
-f(n-1) = f(n-2) + f(n-3) + ... + f(0) ①
+f(n-1) = f(n-2) + f(n-3) + ... + f(0)
 ```
 
-同样，跳上 n 级台阶，可以从 n-1 级跳 1 级上去，也可以从 n-2 级跳 2 级上去...也可以从 0 级跳上去。那么
+同样，跳上 n 级台阶，可以从 n-1 级跳 1 级上去，也可以从 n-2 级跳 2 级上去... ，那么
+
 ```
-f(n) = f(n-1) + f(n-2) + ... + f(0)  ②
+f(n) = f(n-1) + f(n-2) + ... + f(0)
 ```
 
-②-①：
+综上可得
+
 ```
 f(n) - f(n-1) = f(n-1)
+```
+
+即
+
+```
 f(n) = 2*f(n-1)
 ```
 
-所以 f(n) 是一个等比数列：
-```
-f(n) = 2^(n-1)
-```
+所以 f(n) 是一个等比数列
 
-```java
+```source-java
 public int JumpFloorII(int target) {
     return (int) Math.pow(2, target - 1);
 }
 ```
 
+
 # 11. 旋转数组的最小数字
 
 [NowCoder](https://www.nowcoder.com/practice/9f3231a991af4f55b95579b44b7a01ba?tpId=13&tqId=11159&tPage=1&rp=1&ru=/ta/coding-interviews&qru=/ta/coding-interviews/question-ranking)
diff --git a/notes/设计模式.md b/notes/设计模式.md
index dfa0a80d..4e1be4c6 100644
--- a/notes/设计模式.md
+++ b/notes/设计模式.md
@@ -1477,7 +1477,7 @@ public class Client {
 
 ```java
 public interface Subject {
-    void resisterObserver(Observer o);
+    void registerObserver(Observer o);
 
     void removeObserver(Observer o);
 
@@ -1504,7 +1504,7 @@ public class WeatherData implements Subject {
     }
 
     @Override
-    public void resisterObserver(Observer o) {
+    public void registerObserver(Observer o) {
         observers.add(o);
     }
 
@@ -1535,7 +1535,7 @@ public interface Observer {
 public class StatisticsDisplay implements Observer {
 
     public StatisticsDisplay(Subject weatherData) {
-        weatherData.resisterObserver(this);
+        weatherData.reisterObserver(this);
     }
 
     @Override
@@ -1549,7 +1549,7 @@ public class StatisticsDisplay implements Observer {
 public class CurrentConditionsDisplay implements Observer {
 
     public CurrentConditionsDisplay(Subject weatherData) {
-        weatherData.resisterObserver(this);
+        weatherData.registerObserver(this);
     }
 
     @Override
@@ -2558,9 +2558,9 @@ public class Client {
         remoteControl1.off();
         remoteControl1.tuneChannel();
         RemoteControl remoteControl2 = new ConcreteRemoteControl2(new Sony());
-        remoteControl2.on();
-        remoteControl2.off();
-        remoteControl2.tuneChannel();
+         remoteControl2.on();
+         remoteControl2.off();
+         remoteControl2.tuneChannel();
     }
 }
 ```