https://r2.erweima.ai/mathbot/image/1725584157614mxzcxt8i.jpg

The image shows a summation notation, written as:

\[
\sum_{i=1}^{n} i
\]

This is a basic summation formula where you are summing up the values of \( i \) starting from \( i = 1 \) and going up to \( i = n \).

The formula for the sum of the first \( n \) positive integers is given by:

\[
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
\]

This means if you substitute a specific value for \( n \), you can calculate the sum of the integers from 1 to \( n \).

Would you like more details, or do you have any questions?

Here are 5 questions to expand upon this information:
1. What is the summation formula for the sum of squares of the first \( n \) integers?
2. How would you derive the formula for \( \sum_{i=1}^{n} i \)?
3. What happens if we sum over \( i \) from 1 to \( n \), but with each term being \( i^2 \) instead of \( i \)?
4. Can this summation formula be applied to non-integer values of \( n \)?
5. How does this summation relate to triangular numbers in number theory?

**Tip:** Summation formulas are very useful shortcuts for problems involving large series.

Summation notation with limits from i=1 to n: ∑ i

This page explains the summation formula for ∑ i from 1 to n, covering arithmetic series and its formula n(n + 1)/2. Learn how to calculate the sum of the first n natural numbers.

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