Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n

First I would do the base case (the first value):Test n=1,111-6=5. 5 is divisible by 5 therefore true for n=1.
Now we assume true for n=k,11k-6 is divisible by 5.Next we test n=k+1,11k+1-6We can rearrange this into 1111k-6= 1011k+11k-6We know that for n=k the result is 11k-6 which we assume to be true so that part can be assumed to be true.The first part can be factorised into 5(2*11k) which is divisible by 5. Therefore we have shown that if true for n=k, true for n=k+1 and as we shown true for n=1 it must also be true for all natural numbers. So we have proved this through induction

Related Further Mathematics A Level answers

All answers ▸

Show that G = {1, -1} is a group under multiplication.


Prove by induction that for all positive integers n , f(n) = 2^(3n+1) + 3*5^(2n+1) , is divisible by 17.


A particle is projected from the top of a cliff, 20m above the sea level at an angle of 30 degrees above the horizontal at 20m/s. At what vertical speed does it hit the water?


Solve the following inequality: 2x^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