**Mathematical Simplification Example**In this exercise, we aim to simplify a given mathematical expression involving summation notation (Σ). Below is the expression to be simplified:\[ \text{Simplify } \sum_{i=1}^{n} \left( \frac{2i}{n} - \left( \frac{2i}{n} \right)^2 \right) \cdot \frac{2}{n} \]### Explanation:1. **Summation Notation (Σ):** - The summation notation \(\sum_{i=1}^{n}\) indicates that the expression inside the summation symbol should be summed as \(i\) ranges from 1 to \(n\).2. **Inside the Summation:** - The expression inside the summation is \(\left( \frac{2i}{n} - \left( \frac{2i}{n} \right)^2 \right) \cdot \frac{2}{n}\).3. **Breakdown of the Expression:** - \(\frac{2i}{n}\) is a general term that depends on the index \(i\). - \(\left( \frac{2i}{n} \right)^2\) is the square of the term \(\frac{2i}{n}\). - These are subtracted from each other inside the parentheses. - The entire expression \(\left( \frac{2i}{n} - \left( \frac{2i}{n} \right)^2 \right)\) is then multiplied by \(\frac{2}{n}\).### Steps to Simplify:1. **Combine Like Terms:** - Distribute \(\frac{2}{n}\) to both terms inside the parentheses: \[ \sum_{i=1}^{n} \left( \frac{2i}{n} \cdot \frac{2}{n} - \left( \frac{2i}{n} \right)^2 \cdot \frac{2}{n} \right) \] - Simplify each term: \[ \sum_{i=1}^{n} \left( \frac{4i}{n^2} - \frac{8i^2}{n^3} \right) \]2. **Separate

Name: **Mathematical Simplification Example**In this exercise, we aim to si
Uploaded: 2024-03-20T06:38:44.000Z
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Description: **Mathematical Simplification Example**In this exercise, we aim to simplify a given mathematical expression involving summation notation (Σ). Below is the expression to be simplified:\[ \text{Simplify } \sum_{i=1}^{n} \left( \frac{2i}{n} - \left( \f