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Prove the statement by mathematical induction.

The image you provided contains a proof by mathematical induction problem. I'll go ahead and extract the mathematical content for analysis and solve it step by step.

Let me extract the relevant information and solve the induction problem.The image you uploaded appears to be a proof by mathematical induction. Here's how to approach such problems in general:

### Proof by Induction Outline

To prove a statement \( P(n) \) is true for all integers \( n \geq k \) (where \( k \) is the base case), the induction process follows two steps:

1. **Base Case**: Prove that \( P(k) \) is true.
2. **Induction Step**: 
    - Assume \( P(n) \) is true for some arbitrary integer \( n \geq k \) (this is called the induction hypothesis).
    - Prove that \( P(n+1) \) is true under this assumption.

The goal is to show that if the statement is true for \( n \), then it must also be true for \( n+1 \), thereby establishing that the statement holds for all \( n \geq k \).

### Analyzing the Provided Problem

The provided statement in the image is not fully clear, but from the general layout, it appears to follow the steps for proving a formula using induction.

Could you provide a more detailed description of the equation or formula being proven by induction in the image, or would you like me to attempt a solution based on similar common induction proofs?

Explore how to prove statements using mathematical induction. This guide covers the induction process, including setting up a base case and conducting the induction step, with a focus on sequences and series. Suitable for university-level students.

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