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The inductive step of an inductive proof shows that for k > 4, if 2k > 3k,, then 2k+> 3 (k + 1). In which step of the proof is the inductive hypothesis used? 2k+1 2. 2k (Step 1) 2 2.3k (Step 2) > 3k + 3k (Step 3) 2 3k + 3 (Step 4) 2 3 (k+ 1) (Step 5) O Step 1 O Step 2 Step 4 O Step 3

The inductive step of an inductive proof shows that for k > 4, if 2k > 3k,, then 2k+> 3 (k + 1). In which step of the proof is the inductive hypothesis used? 2k+1 2. 2k (Step 1) 2 2.3k (Step 2) > 3k + 3k (Step 3) 2 3k + 3 (Step 4) 2 3 (k+ 1) (Step 5) O Step 1 O Step 2 Step 4 O Step 3

Advanced Engineering Mathematics
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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**Inductive Step of an Inductive Proof** The inductive step of an inductive proof shows that for \( k \geq 4 \), if \( 2^k \geq 3k \), then \( 2^{k+1} \geq 3(k + 1) \). **In which step of the proof is the inductive hypothesis used?** 1. \( 2^{k+1} \geq 2 \cdot 2^k \) (Step 1) 2. \( \geq 2 \cdot 3k \) (Step 2) 3. \( \geq 3k + 3k \) (Step 3) 4. \( \geq 3k + 3 \) (Step 4) 5. \( \geq 3(k + 1) \) (Step 5) **Options:** - ○ Step 1 - ● Step 2 - ○ Step 4 - ○ Step 3
Transcribed Image Text:**Inductive Step of an Inductive Proof** The inductive step of an inductive proof shows that for \( k \geq 4 \), if \( 2^k \geq 3k \), then \( 2^{k+1} \geq 3(k + 1) \). **In which step of the proof is the inductive hypothesis used?** 1. \( 2^{k+1} \geq 2 \cdot 2^k \) (Step 1) 2. \( \geq 2 \cdot 3k \) (Step 2) 3. \( \geq 3k + 3k \) (Step 3) 4. \( \geq 3k + 3 \) (Step 4) 5. \( \geq 3(k + 1) \) (Step 5) **Options:** - ○ Step 1 - ● Step 2 - ○ Step 4 - ○ Step 3
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