Show using mathematical induction that 8^n - 1 is divisible by 7 for n=1,2,3,...

First step: n=1 we have 81 -1=7 which is divisible by 7. Assumption step: 8k-1 is divisible by 7. Induction step: Using the previous step we have that 8k-1=7x. So 8k = 7x+1. Therefore, 8k+1- 1=8(8k)-1=8(7x+1)-1 = 56x + 8 -1 = 56x+7 = 7(8x+1) which is divisible by 7. Hence, since it is true for n=1, n = k and for n=k+1 then it is true for all positive integers

Answered by Mike C. Maths tutor

4672 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the stationary points of a curve?


The curve C has equation: 2x^2y + 2x + 4y – cos (piy) = 17. Use implicit differentiation to find dy/dx in terms of x and y.


What is the factor theorem?


Find the derivative of x^3 - (y^2)x =3


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences