https://file.aiquickdraw.com/mathbot/file/1725449566719akyecwdl.jpg

The image you've uploaded appears to be a mathematics test or worksheet. I'll help you by analyzing the content and addressing the questions or problems presented. Let's begin by extracting the relevant mathematical content from the image.

### Content Extracted:
1. **Problem 1 (INDUCTION):**
   - There is a problem about induction. It asks to **"Prove by mathematical induction"** the given expression or equation. The steps for induction (base case and inductive step) are indicated.

2. **Problem 2:**
   - This section has multiple-choice questions with equations that likely need to be simplified or evaluated.

3. **Problem 3 (CIRCULAR FUNCTION):**
   - This problem seems to be about circular or trigonometric functions, asking to evaluate an expression.

Let me know which specific problem you'd like to solve or if you'd like to go through each one systematically.

Prove by mathematical induction that for all n ≥ 1, the sum of the first n odd numbers is equal to n^2.

Explore how to prove the sum of the first n odd numbers equals n^2 using the principle of mathematical induction. This step-by-step guide is ideal for students in Grades 11-12, covering key concepts in sequences, series, and mathematical induction.

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