DOC: DataFrame.update doctests (#56219)

* Add doctest showing dtype changing

* Fix docstring results

* Tidy

* Remove docs for changing dtype

pandas/core/frame.py

@@ -8826,26 +8826,27 @@ def update(
         1  b  e
         2  c  f
 
-        For Series, its name attribute must be set.
-
         >>> df = pd.DataFrame({'A': ['a', 'b', 'c'],
         ...                    'B': ['x', 'y', 'z']})
-        >>> new_column = pd.Series(['d', 'e'], name='B', index=[0, 2])
-        >>> df.update(new_column)
+        >>> new_df = pd.DataFrame({'B': ['d', 'f']}, index=[0, 2])
+        >>> df.update(new_df)
         >>> df
            A  B
         0  a  d
         1  b  y
-        2  c  e
+        2  c  f
+
+        For Series, its name attribute must be set.
+
         >>> df = pd.DataFrame({'A': ['a', 'b', 'c'],
         ...                    'B': ['x', 'y', 'z']})
-        >>> new_df = pd.DataFrame({'B': ['d', 'e']}, index=[1, 2])
-        >>> df.update(new_df)
+        >>> new_column = pd.Series(['d', 'e', 'f'], name='B')
+        >>> df.update(new_column)
         >>> df
            A  B
-        0  a  x
-        1  b  d
-        2  c  e
+        0  a  d
+        1  b  e
+        2  c  f
 
         If `other` contains NaNs the corresponding values are not updated
         in the original dataframe.