Question
What is the sum of the first 1000 natural numbers
Ask by Erickson Bernard. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum of the first 1,000 natural numbers is 500,500.
Solution
The sum of the first 1,000 natural numbers can be calculated using the formula for the sum of an arithmetic series. Here's how you can do it:
**Formula:**
\[
\text{Sum} = \frac{n(n + 1)}{2}
\]
Where:
- \( n \) is the number of terms to be added.
**Applying the Formula:**
\[
n = 1000
\]
\[
\text{Sum} = \frac{1000 \times (1000 + 1)}{2} = \frac{1000 \times 1001}{2}
\]
**Calculating:**
\[
\frac{1000 \times 1001}{2} = \frac{1,001,000}{2} = 500,500
\]
**Answer:**
The sum of the first 1,000 natural numbers is **500,500**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Did you know that the formula to find the sum of the first \( n \) natural numbers is \( \frac{n(n + 1)}{2} \)? So for the first 1000 natural numbers, just plug in 1000: \( \frac{1000 \times (1000 + 1)}{2} = \frac{1000 \times 1001}{2} \), which gives you 500500. That’s right, the sum is 500,500! Now, imagine trying to add those up individually! It might take ages and a lot of patience. Instead, using this nifty formula not only saves time but also minimizes mistakes. It’s a classic example of how mathematics can simplify our lives. Next time you need to sum a series of numbers, think about how you can apply this formula; your future self will thank you!
