https://r2.erweima.ai/mathbot/image/1725871100563bnktqlgj.jpg

Let's analyze the image.

The problem is asking for the sum of squares of consecutive integers from 1 to 100, expressed using Sigma (summation) notation. The sum is:

\[
1^2 + 2^2 + 3^2 + \dots + 99^2 + 100^2
\]

This is the sum of squares of the first 100 integers, which can be written in Sigma notation as:

\[
\sum_{i=1}^{100} i^2
\]

Looking at the options provided, the correct expression corresponds to the third choice:

\[
\sum_{i=1}^{100} i^2
\]

Let me know if you'd like more details or have any questions.

Here are five related questions for further exploration:
1. How would you find the sum of squares formula for the first \(n\) integers?
2. What is the general formula for the sum of the first \(n\) squares?
3. How does the sum of cubes differ from the sum of squares?
4. Can you express the sum of even squares from 2 to 100 using sigma notation?
5. How would the sigma notation change if you were asked to sum cubes instead of squares?

**Tip:** The sum of squares for the first \(n\) integers has a closed-form formula: \(\frac{n(n+1)(2n+1)}{6}\).

Use Sigma notation to find an expression for the sum of squares of consecutive integers from 1 to 100.

Learn how to express the sum of squares of consecutive integers from 1 to 100 using Sigma notation. This problem covers key mathematical concepts such as summation notation and the sum of squares formula. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation