QCEVault

Proof and induction — Question 23

Original QCE Vault practice · 1 mark

Q23 · Practice questionSimple familiar1 mark

QUESTION 23

Assume 7k−17^k-1 is divisible by 6. Which rearrangement is most useful for the inductive step?
(A)
7k+1−1=7(7k−1)+67^{k+1}-1=7(7^k-1)+6
(B)
7k+1−1=6(7k−1)+17^{k+1}-1=6(7^k-1)+1
(C)
7k+1−1=7k+67^{k+1}-1=7^k+6
(D)
7k+1−1=(7k−1)27^{k+1}-1=(7^k-1)^2
Question linkSyllabus coverage

Related questions

  1. Q4 · Original practice · 1 mark
    Original Specialist Mathematics practice question 4: induction and divisibility
    Proof and induction
  2. Q18 · Original practice · 5 marks
    Use mathematical induction to prove that ∑r=1nr(r+1)=n(n+1)(n+2)3\sum_{r=1}^n r(r+1)=\frac{n(n+1)(n+2)}3 for every positive integer nn.
    Proof and induction
  3. Q20 · Original practice · 5 marks
    Use mathematical induction to prove that 8n−2n8^n-2^n is divisible by 6 for every positive integer nn.
    Proof and induction
  4. Q21 · Original practice · 1 mark
    In proving 1+3+⋯+(2n−1)=n21+3+\cdots+(2n-1)=n^2 by induction, the left side for n=k+1n=k+1 becomes
    Proof and induction