Prove by mathematical induction that11×2×3+12×3×4+ ⋯ +1n(n+1)(n+2)=14−12(n+1)(n+2).

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Prove by mathematical induction that11×2×3+12×3×4+ ⋯ +1n(n+1)(n+2)=14−12(n+1)(n+2).
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Solution 1

Sure, let's prove the given statement using the principle of mathematical induction.

Mathematical induction has two steps: the base case and the inductive step.

Step 1: Base Case Let's start with n=1. The left side of the equation becomes 11×2×3 = 6, and the right side becomes 1/4 - 1/2(1+1)(1+2) Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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