Without doing the actual addition, find the sum of:
`1 + 3 + 5 + 7 + 9 + 11+ 13 + 15 + 17+ 19 + 21 + 23`

Explanation

To find the sum of the series \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\) without doing the actual addition, we can use the property of the sum of odd numbers.

### Step-by-Step Solution:

1. **Identify the Sequence**:
The numbers given are all odd numbers starting from 1 up to 23.

2. **Count the Numbers**:
We need to count how many odd numbers are there in the sequence. The sequence is:
\[ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 \]
Counting these, we find there are 12 numbers.

3. **Use the Formula for the Sum of Odd Numbers**:
The sum of the first \(n\) odd numbers is given by the formula:
\[ \text{Sum} = n^2 \]
where \(n\) is the number of terms.

4. **Calculate the Sum**:
Since we have 12 odd numbers, we substitute \(n = 12\) into the formula:
\[ \text{Sum} = 12^2 = 144 \]

5. **Final Answer**:
Therefore, the sum of the series \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\) is \(144\).