QCEVault

Proof and induction — Question 4

Original QCE Vault practice · 1 mark

Q4 · Practice questionSimple familiar1 mark

QUESTION 4

Which expression is divisible by 5 for every positive integer nn?

(A)
5n−15^n-1
(B)
4n−14^n-1
(C)
22n−12^{2n}-1
(D)
6n−16^n-1
Question linkSyllabus coverage

Related questions

  1. 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
  2. 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
  3. 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
  4. Q22 · Original practice · 6 marks
    View question and marking material
    Proof and induction