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    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?
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    (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?
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    (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)}
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    (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)
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    (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.
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    (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
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      (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
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      (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}
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      (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
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      (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!!!

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