Prove the following statement using induction. 1. For all positive integers n, n < 2". Hint: Note that 1 <2k for all positive integers k. For this proof, answer the following questions: Complete the basis step of the proof. • What is the inductive hypothesis? What do you need to show in the inductive step of the proof Complete the inductive step of the proof.

Prove the following statement using induction. 1. For all positive integers n, n < 2". Hint: Note that 1 <2k for all positive integers k. For this proof, answer the following questions: Complete the basis step of the proof. • What is the inductive hypothesis? What do you need to show in the inductive step of the proof Complete the inductive step of the proof.

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

Prove the following statement using induction.
1.
For all positive integers n, n < 2".
Hint: Note that 1 < 2k for all positive integers k.
For this proof, answer the following questions:
• Complete the basis step of the proof.
• What is the inductive hypothesis?
What do you need to show in the inductive step of the proof?
Complete the inductive step of the proof.

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Step 1: Define induction

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