Mathematical Induction of 4 + 14 + ... + n(3n+1) = n(n+1)^2 скачать в хорошем качестве

Mathematical Induction of 4 + 14 + ... + n(3n+1) = n(n+1)^2

📚 Mathematical Induction: [4+ 14 + \dots + n(3n+1) = n(n+1)^2] In this lesson, we use *mathematical induction* to prove a more advanced summation formula involving quadratic terms. We show step by step how to: Identify the general term of the sequence Prove the *base case* Set up the *inductive hypothesis* Complete the *inductive step* Reach the final conclusion using induction This example helps you understand how induction works with more complex expressions, not just simple sums. What you will learn: How to apply induction to quadratic expressions How to factor and simplify during the inductive step How patterns in algebra help complete proofs --- ✏️ *Try it yourself:* Before watching the full solution, check the formula for: (n = 1) (n = 2) See if both sides match. If you find this lesson helpful: 👍 Like the video 🔔 Subscribe for more mathematics lessons 📤 Share with your classmates #MathematicalInduction #MathProof #Summation #DiscreteMathematics