**Finding the Sum of 19782 and 9999 using a Short Method**

To find the sum of 19782 and 9999 using a short method, we can use a technique called vertical addition or column addition. This method allows us to add the digits of each place value column separately and carry any excess to the next column.

Here's how we can do it step by step:

Step 1: Write the numbers in a vertical format with the units digits aligned.

```
19782
+ 9999
```

Step 2: Start adding the digits in the rightmost column (units column).

```
19782
+ 9999
--------
1
```

Step 3: Move to the next column (tens column) and add the digits.

```
19782
+ 9999
--------
81
```

Step 4: Continue adding the digits in the next column (hundreds column).

```
19782
+ 9999
--------
781
```

Step 5: Add the digits in the thousands column.

```
19782
+ 9999
--------
9791
```

Step 6: Finally, add the digits in the ten thousands column.

```
19782
+ 9999
--------
29791
```

Therefore, the sum of 19782 and 9999 is 29791.

Using this short method of vertical addition, we can quickly and efficiently find the sum of two numbers. It is important to align the digits properly in each place value column and carry any excess to the next column as needed.

This method becomes especially useful when dealing with larger numbers, as it allows us to break down the addition process into manageable steps and reduces the chances of making errors.