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Further Pure 1 help watch

1. 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?
2. (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?
3. (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
4. (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?
(Original post by RDKGames)
Basic GCSE indices
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)
5. (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

Then, as RDKGames said.
6. (Original post by ghostwalker)
For any number, call it x, we have x+x = 2x.

So, here

Then, as RDKGames said.
Okay but how do we know those two equal each other?
Like I expect 2^k + 2^k to be something else? Sorry i am really stuck
7. (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?
8. (Original post by English-help)
Okay but how do we know those two equal each other?
Like I expect 2^k + 2^k to be something else? Sorry i am really stuck
Perhaps a specific example will help.

Or putting it another way

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

Its like saying or
10. (Original post by RDKGames)
What do you mean? You are adding to itself once so you have 2 lots of

Its like saying or
(Original post by ghostwalker)
Perhaps a specific example will help.

Or putting it another way

Dw i get it! Thankss!!!

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