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

    0
    ReputationRep:
    Hi guys,

    I wonder if anybody could help me do an FP1 question on Induction ( q.10, p.105, ex.6)

    The question is:

    "Prove that if Un+2=3Un+1 -2Un for n being an element of the set of natural numbers, and if U1=1 , U2=3, then Un=(2^n)-1."

    Could someone please walk me through the steps of the solution? - I have no idea how to do a question with a Un+2 in. I know how to do it if there is an expression connecting Un+1 and Un

    Thanks a lot in advance!!
    • PS Helper
    Offline

    14
    PS Helper
    This is an induction question with 2 base cases. Usually you have one base case and you have to show that {true for k} implies {true for k+1}, whereas here you need to show that {true for k and k+1} implies {true for k+2}. So check that it holds true for the base cases (u_1 and u_2), and then check that if it's true for n=k,k+1 then it's true for n=k+2.

    That is, given that u_k=2^k-1 and u_{k+1}=2^{k+1}-1, show that u_{k+2}=2^{k+2}-1 using the formula.
 
 
 
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.