Turn on thread page Beta
    • Thread Starter
    Offline

    15
    ReputationRep:
    https://jacktilson.net/edu/maths/mar...ummer-2005.pdf
    If you go to page 25 and look at Question 5 , it doesnt make sense to me?
    Can someone help?
    Basically in the first line it says 2^(k) + 2^(k) -1 = 2^(k+1) -1 and then says 2.2^(k)= 2^(k+1)
    Can someone explain it to me please?
    • Very Important Poster
    Offline

    21
    ReputationRep:
    Very Important Poster
    (Original post by English-help)
    https://jacktilson.net/edu/maths/mar...ummer-2005.pdf
    If you go to page 25 and look at Question 5 , it doesnt make sense to me?
    Can someone help?
    Basically in the first line it says 2^(k) + 2^(k) -1 = 2^(k+1) -1 and then says 2.2^(k)= 2^(k+1)
    Can someone explain it to me please?
    If we say a= 2^k

    Then we have a + a -1. This becomes 2a - 1.

    Put a back in to give 2* (2^k) + 1.

    Then use what you know to get the 2^(k+1) from this statement.

    Is this the part that needed clarifying?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by English-help)
    https://jacktilson.net/edu/maths/mar...ummer-2005.pdf
    If you go to page 25 and look at Question 5 , it doesnt make sense to me?
    Can someone help?
    Basically in the first line it says 2^(k) + 2^(k) -1 = 2^(k+1) -1 and then says 2.2^(k)= 2^(k+1)
    Can someone explain it to me please?
    Basic GCSE indices
    2\cdot 2^k = 2^1 \cdot 2^k = 2^{(1+k)}
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by SeanFM)
    If we say a= 2^k

    Then we have a + a -1. This becomes 2a - 1.

    Put a back in to give 2* (2^k) + 1.

    Then use what you know to get the 2^(k+1) from this statement.

    Is this the part that needed clarifying?
    Read the bottom reply Sean
    (Original post by RDKGames)
    Basic GCSE indices
    2\cdot 2^k = 2^1 \cdot 2^k = 2^{(1+k)}
    Its the 2^k +2^k that is not making sense tbh , like i know the part you said , that makes sense to me , its the top part how 2^k + 2^k= 2^(k+1)
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by English-help)
    Its the 2^k +2^k that is not making sense tbh , like i know the part you said , that makes sense to me , its the top part how 2^k + 2^k= 2^(k+1)
    For any number, call it x, we have x+x = 2x.

    So, here 2^k +2^k = 2\cdot 2^k

    Then, as RDKGames said.
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by ghostwalker)
    For any number, call it x, we have x+x = 2x.

    So, here 2^k +2^k = 2\cdot 2^k

    Then, as RDKGames said.
    Okay but how do we know those two equal each other? :confused:
    Like I expect 2^k + 2^k to be something else? Sorry i am really stuck
    Offline

    19
    ReputationRep:
    (Original post by SeanFM)
    If we say a= 2^k

    Then we have a + a -1. This becomes 2a - 1.

    Put a back in to give 2* (2^k) + 1.

    Then use what you know to get the 2^(k+1) from this statement.

    Is this the part that needed clarifying?
    This should help you OP
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by English-help)
    Okay but how do we know those two equal each other? :confused:
    Like I expect 2^k + 2^k to be something else? Sorry i am really stuck
    Perhaps a specific example will help.

    2^5+2^5= 2\times 2^5 = 2^1\times 2^5=2^{5+1}=2^6

    Or putting it another way

    2^5+2^5=32+32=64=2^6=2^{5+1}
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by English-help)
    Okay but how do we know those two equal each other? :confused:
    Like I expect 2^k + 2^k to be something else? Sorry i am really stuck
    What do you mean? You are adding 2^k to itself once so you have 2 lots of 2^k

    Its like saying 1+1=2 \cdot 1 = 2 or 2+2+2=3\cdot 2 = 6
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by RDKGames)
    What do you mean? You are adding 2^k to itself once so you have 2 lots of 2^k

    Its like saying 1+1=2 \cdot 1 = 2 or 2+2+2=3\cdot 2 = 6
    (Original post by ghostwalker)
    Perhaps a specific example will help.

    2^5+2^5= 2\times 2^5 = 2^1\times 2^5=2^{5+1}=2^6

    Or putting it another way

    2^5+2^5=32+32=64=2^6=2^{5+1}
    Dw i get it! Thankss!!!

    Posted from TSR Mobile
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 14, 2017

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.