**Title: Verifying Candidate Solutions Using Induction****Objective:**Use induction to verify the candidate solution for the following recurrence relation:\[ T(n) = T(n-1) + \frac{1}{n(n+1)} \quad \text{for } n > 1 \]**Base Case:**\[ T(1) = \frac{1}{2} \]**Candidate Solution:**The candidate solution is proposed as:\[ T(n) = \frac{n}{n+1} \]**Instructions:**1. Verify the base case by substituting \( n = 1 \) into the candidate solution.2. Use mathematical induction to prove that the solution holds for all \( n > 1 \).3. Demonstrate the step-by-step inductive proof and ensure the calculations align with the recurrence relation.

The given recurrence relation Tn=Tn-1+1nn+1, for n>1 T1=12 We have to prove the candidate…

Answered: Use induction to verify the candidate…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use induction to verify the candidate solution for the following recurrence relation: 1 for n > 1 n(n + 1)' T(n) = T(n-1) + 1 T(1) 2 with canidate solution T(n) = 1 =