Understanding the Sum of Numbers
To solve the expression \(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 16 + 17\), we can break it down into manageable parts.
Grouping the Numbers
- The numbers can be grouped for easier calculation. Notice that we are missing the number 15 in this sequence.
Calculating the Sum
- First, we can calculate the sum of all numbers from 1 to 17, and then subtract 15.
Formula for Summation
- The formula for the sum of the first \(n\) natural numbers is given by:
\[
\text{Sum} = \frac{n(n + 1)}{2}
\]
- For \(n = 17\):
\[
\text{Sum} = \frac{17(17 + 1)}{2} = \frac{17 \times 18}{2} = 153
\]
Subtracting the Missing Number
- Now, subtract the missing number 15 from the total sum:
\[
153 - 15 = 138
\]
Final Result
- Therefore, the total sum of the numbers \(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 16 + 17\) is:
\[
\text{Total Sum} = 138
\]
Conclusion
- The step-by-step breakdown helps in understanding how to approach summing a series of numbers, especially when one is missing. This method can be applied to various math problems in your studies.