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

MC
Answered by Mike C. Maths tutor

4857 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A function is defined parametrically as x = 4 sin(3t), y = 2 cos(3t). Find and simplify d^2 y/dx^2 in terms of t and y.


Solve: 2 sin(2x) = (1-sin(x))cos(x) for 0<x<2*Pi and give any values of x, if any, where the equation is not valid


Consider the functions f(x) = −x^3 + 2x^2 + 3x and g(x) = −x^3 + 3x^2 − x + 3. (a) Find df/dx (x) and hence show that f(x) has turning points at when x = 2 /3 ± √ 13/ 3 . [5] (b) Find the points where f(x) and g(x) intersect. [4]


What is the integral of x sin(x) dx?


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