Prove a(n) ≤ 3^n Using Induction | VTU Exam Problem

Learn Mathematical Induction with an important VTU problem involving recursive relations, explained step-by-step. Perfect for BCS405A students to understand recurrence-based proofs and score high in exams. ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question: ❓ Given that a(0) = 1, a(1) = 2, a(2) = 3, and a(n) = a(n − 1) + a(n − 2) + a(n − 3), for n ≥ 3, prove that a(n) ≤ 3^n, for all n ∈ ℤ⁺. 📆 Asked in: • Dec 2024 / Jan 2025 – Question 3(b) • Model Question Paper 1 – Question 4(a) 📘 Subject: Discrete Mathematical Structures 📚 Subject Code: BCS405A 📌 Module 2 – Properties of the Integers 📝 Topic: Recursive Relations (Mathematical Induction) ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: • Recursive definition of sequences • Applying induction to recurrence relations • Bounding sequences using inequalities • Step-by-step inductive reasoning • Solving VTU exam questions efficiently ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ Next Video (Binomial Theorem Basics)    • Complete Guide: Binomial & Multinomial The...   2️⃣ Continue Learning    • Score Full Marks on Binomial Theorem | VTU...   3️⃣ More Practice    • Must-Know Trick for Multinomial Theorem | ...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): BCS405A Module 2 – Discrete Mathematics    • BCS405A Module 2( Discrete Mathematics )   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Topics: 1️⃣ Strong Induction    • BCS405A Mathematical Induction Problem #9 ...   2️⃣ Divisibility Proof    • BCS405A Mathematical Induction Problem #8 ...   3️⃣ Inequality Problems    • BCS405A Mathematical Induction Problem #6 ...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Move to binomial theorem and coefficient problems. 📌 Don’t stop here: Practice more recursive problems to strengthen your understanding. ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ 📙 All BCS405A Playlists: ▶️ Module 1 – Fundamentals of Logic (Model Papers)    • BCS405A Module 1 – Fundamentals of Logic |...   ▶️ Module 1 – Full Concepts    • BCS405A Module 1 ( Fundamentals of Logic )   ▶️ Module 2 – Mathematical Induction    • BCS405A Module 2( Discrete Mathematics )   ▶️ Module 3 – Relations and Functions    • Relations and Functions | BCS405A Module 3...   ▶️ Module 4 – Recurrence & Inclusion-Exclusion    • BCS405A Module 4  ( The principle of exclu...   ▶️ Module 5 – Group Theory    • BCS405A Module 5 (Group Theory)   ━━━━━━━━━━━━━━━━━━━━━ #DiscreteMathematics #BCS405A #RecurrenceRelation #MathematicalInduction #VTUMaths #EngineeringMaths #VTUExam