Problem 2. Let n ∈ N. Prove the formula using mathematical induction: 1 · 2 · 3 + 2 · 3 · 4 + · · · + n(n + 1)(n + 2) = 1 4 n(n + 1)(n + 2)(n + 3). Problem 2. Let n E N. Prove the formula using mathematical induction:1.2.3+2.3.4+...+ n(n+1)(n+2)=n(n+1)(n+2)(n+3).

Given : 1·2·3+2·3·4 + · · · · · ·+nn+1n+2=14nn+1n+2n+3 , n∈ℕ To Prove : Given equation by…

Answered: Problem 2. Let n E N. Prove the formula…

Problem 2. Let n E N. Prove the formula using mathematical induction: 1 1.2.3+2.3.4+ + n(n+1)(n+ 2) = = n(n+1)(n+2)(n+3).

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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Question

Problem 2. Let n ∈ N. Prove the formula using mathematical induction: 1 · 2 · 3 + 2 · 3 · 4 + · · · + n(n + 1)(n + 2) = 1 4 n(n + 1)(n + 2)(n + 3).

Problem 2. Let n E N. Prove the formula using mathematical induction:
1.2.3+2.3.4+...+ n(n+1)(n+2)
=
n(n+1)(n+2)(n+3).

Expert Solution

Step 1

Given : $1 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot 4 + \cdot \cdot \cdot \cdot \cdot \cdot + n (n + 1) (n + 2) = \frac{1}{4} n (n + 1) (n + 2) (n + 3), n \in ℕ$

To Prove : Given equation by mathematical induction

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(i)There are 18 mathematics majors and 325 computer science majors at a college.In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? (Ii) Prove by mathematical induction that: 1+(1/√2)+(1/√3)+....+(1/√n)<=2√n
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You are asked to prove that 12+ 22 + 32 + ·..+n? n(n+1)(2n+1) %3D using the Principle of Mathematical Induction. Which of the following is the correct assumption for the inductive step? O Assume that the equation (k-1)[(k-1)+1][2(k-1)+1] 1 + 22 + 32 + ·..+ (k – 1)² = (k-1)(k)(2k-1) %3D 6 is true. O Assume that the equation 12 = 1 = 123 1(1+1)(2-1+1) %3D is true. O Assume that the equation 12 + 22 + 32 + ..+ k² + (k + 1)² [k+1][(k+1)+1][2(k+1)+1] (k+1)(k+2)(2k+3) is true. O Assume that the equation 12 + 22 + 32 + ...+ k² = k(k+1)(2k+1) %3D 6. is true.
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This is a practice question from my Discrete Mathematical Structures Course. Thank you.
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Problem 8 Use Mathematical Induction to prove that 1² + 3² +5² +...+(2n + 1)² = whenever n is a nonnegative integer. (n + 1) (2n + 1)(2n + 3) 3 P
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