Question:

Emma Jane made an error proving that 2 3 1 n  is divisible by 8 (for n t1), using mathematical induction. Part of her proof is shown below. Step 2: Assume the result true for n=k             32k-1=8P  where P is an integer             Hence 32k=8P+1 Step 3: To prove the result is true for n=k+1            RTP:32(k+1)-1=8Q where Q is an integer.   Line 1           LHS=32k+2-1                                              Line 2                 =32k×32-1                 =(8P+1)×32-1 (using the assumption)  Line 3                 =72P+1-1                                             Line 4                 =8(9P)                 =8Q                 =RHS In which line did Emma Jane make an error? A) Line 1 B) Line 2 C) Line 3 D) Line 4 

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Proof - Mathematical Induction
Paper 1

10 Questions/Answers

Proof - Mathematical Induction
Paper 2

10 Questions/Answers

Proof - Mathematical Induction
Paper 3

10 Questions/Answers

Proof - Mathematical Induction
Paper 4

10 Questions/Answers

Proof - Mathematical Induction
Paper 5

10 Questions/Answers

Proof - Mathematical Induction
Paper 6

10 Questions/Answers

Proof - Mathematical Induction
Paper 7

10 Questions/Answers

Proof - Mathematical Induction
Paper 8

10 Questions/Answers

Proof - Mathematical Induction
Paper 9

10 Questions/Answers

Proof - Mathematical Induction
Paper 10

10 Questions/Answers

Proof - Mathematical Induction
Paper 11

10 Questions/Answers

Proof - Mathematical Induction
Paper 12

10 Questions/Answers

Proof - Mathematical Induction
Paper 13

10 Questions/Answers

Proof - Mathematical Induction
Paper 14

10 Questions/Answers

Proof - Mathematical Induction
Paper 15

10 Questions/Answers

Proof - Mathematical Induction
Paper 16

10 Questions/Answers

Proof - Mathematical Induction
Paper 17

10 Questions/Answers

Proof - Mathematical Induction
Paper 18

10 Questions/Answers

Proof - Mathematical Induction
Paper 19

10 Questions/Answers

Proof - Mathematical Induction
Paper 20

10 Questions/Answers

Proof - Mathematical Induction
Paper 21

10 Questions/Answers

Proof - Mathematical Induction
Paper 22

10 Questions/Answers

Proof - Mathematical Induction
Paper 23

10 Questions/Answers

Proof - Mathematical Induction
Paper 24

10 Questions/Answers