Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    11
    ReputationRep:
    And finally I am stuck after 50 or so questions... :p:
    Can someone explain where I'm going wrong :brick:
    Sorry I don't know how to use latex, but will bother to learn eventually...:rolleyes:

    Okay this is what I've done so far...

    Prove that 8^n - 3^n is divisible by 5 [for all positive integers of n blah blah].

    Let f(n) = 8^n - 3^n
    When n = 1,
    f(1) = 8 - 3 = 5, which is divisible by 5.
    Therefore, f(n) is divisible exactly by 5 when n=1.

    Assume the general statement is true when n=k i.e.:
    f(k) = 8^k - 3^k is divisible by 5.

    When n = k + 1
    f(k+1) - f(k) = 8^(k+1) - 3^(k+1) - (8^k - 3^k)
    = 8.8^k - 8^k - 3.3^k + 3^k
    = 8^k(8 - 1) - [3.3^k - 3^k]
    = 8^k(8-1) - [3^k(3 - 1)]
    = 7.8^k - 2.3^k

    Now where do I go from here!? Thanks!!
    • Thread Starter
    Offline

    11
    ReputationRep:
    booooooooooooomp
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    ...= 5.8^k + 2.8^k - 2.3^k = 5.8^k + 2(8^k-3^k) = 5.8^k + 2f(k)
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by Magician)
    where did u get the 5 from?
    As in 7.8^k = 5.8^k + 2.8^k.

    Makes sense now.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Magician)
    where did u get the 5 from?
    7.8^k = 5.8^k +2.8^k
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.