Simple Year 10 Mathematics Problem Help (1 Viewer)

[jack2230]

After browsing the forums it seems BOS has some math geniuses who may be able to help with this math question I have. Hopefully this thread is in the correct section because as it is around the Year 10 math syllabus, I thought it would be inappropriate to place it under Mathematics or Extension 1. I would greatly appreciate anyone with some insight though and thank you in advance.

<a href="http://www.codecogs.com/eqnedit.php?latex=Show&space;that:&space;2(2^{k}-1)&space;&plus;&space;2^{k&plus;1}&space;=&space;2(2^{k&plus;1}-1)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?Show&space;that:&space;2(2^{k}-1)&space;&plus;&space;2^{k&plus;1}&space;=&space;2(2^{k&plus;1}-1)" title="Show that: 2(2^{k}-1) + 2^{k+1} = 2(2^{k+1}-1)" /></a>

Jack

 

[Menomaths]

when the bases are same and you are multiplying, you add the powers so



Now we simplify

 

[HAX0R]

2(2^(k+1)-1)+2^k+1

Is equal to 2^(2k+1)-2+2^(k+1)
Let x be 2^(k+1). (If you don't understand)
x-2+x
2x-2

On the right hand side: 2(2^(k+1)-1) is equal to: 2(x-1)
Which is equal to 2x-2.
Which is equal to left hand side.

<a href="http://www.codecogs.com/eqnedit.php?latex=2(2^{k}-1)&plus;2^{k&plus;1}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?2(2^{k}-1)&plus;2^{k&plus;1}" title="2(2^{k}-1)+2^{k+1}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==2\times2^{k&plus;1}-2" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=2\times2^{k&plus;1}-2" title="=2\times2^{k+1}-2" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==2(2^{k&plus;1}-1)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=2(2^{k&plus;1}-1)" title="=2(2^{k+1}-1)" /></a>

 

[jack2230]

Thanks very much, that explains it nicely.

Thanks,
Jack