Use the formula S 

​=StartFraction n left parenthesis n plus 1 right parenthesis Over 2 EndFractionn(n + 1)2 

to find the sum of 1​ + 2​ + 3​ + ...​ + 

970970.

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Part 1

1​ + 2​ + 3​ + ...​ + 

970970 

​= enter your response here

To find the sum of the series \( 1 + 2 + 3 + \dots + 970 \), we can use the formula \( S = \frac{n(n+1)}{2} \).

Here, \( n = 970 \).

Let's calculate the sum:

\[
S = \frac{970(970 + 1)}{2}
\]

\[
S = \frac{970 \times 971}{2}
\]

\[
S = \frac{941870}{2}
\]

\[
S = 470935
\]

So, the sum \( 1 + 2 + 3 + \dots + 970 \) is \( 470,935 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the sum change if the series went up to 1000 instead of 970?
2. What is the sum of the first 500 natural numbers?
3. How does the sum formula change if you sum from 2 to 970 instead of 1 to 970?
4. Can this method be used for summing negative integers?
5. How would you find the sum of the first \( n \) odd numbers?

**Tip:** When calculating large sums, ensure you carefully handle multiplication and division to avoid errors, especially when \( n \) is large.

Learn how to calculate the sum of numbers from 1 to 970 using the formula S = n(n + 1) / 2. This problem involves finding the sum of an arithmetic series and is suitable for students in Grades 7-9.

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