Use the formula S ​=StartFraction n left parenthesis n plus 1 right parenthesis Over 2 EndFraction
to find the sum of 1​ + 2​ + 3​ + ...​ + 880.
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Part 1
1​ + 2​ + 3​ + ...​ + 880 ​=

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The formula provided, \( S = \frac{n(n+1)}{2} \), is used to find the sum of the first \( n \) natural numbers. 

In this case, the sum of the series \( 1 + 2 + 3 + \dots + 880 \) can be calculated by setting \( n = 880 \).

Let's apply the formula:

\[
S = \frac{880(880 + 1)}{2}
\]

\[
S = \frac{880 \times 881}{2}
\]

\[
S = \frac{774080}{2}
\]

\[
S = 387440
\]

So, the sum \( 1 + 2 + 3 + \dots + 880 \) is \( 387,440 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How does this formula change if the series does not start from 1?
2. What is the sum of the first 1000 natural numbers?
3. How would you find the sum of an arithmetic series that has a common difference other than 1?
4. Can this formula be used for non-consecutive numbers?
5. How do you derive the formula for the sum of the first \( n \) natural numbers?

**Tip:** The formula \( S = \frac{n(n+1)}{2} \) is a quick way to sum up consecutive integers starting from 1. It's a valuable tool for solving problems efficiently!

Learn how to calculate the sum of the series 1 + 2 + 3 + ... + 880 using the formula S = n(n + 1) / 2. Follow a step-by-step solution to find the total sum efficiently. Suitable for Grades 6-8 students.

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