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FP2 series question

Any help on the following would be greatly received.. (I know it's late!)

(JAN 2010 AQA)

Q 7. b)

Screen Shot 2014-06-18 at 00.20.16.png

I don't understand how they go from the 1st line to the 2nd line in the mark scheme. I of course get the 'n' part, but not how they automatically get 3(2^n -1)

Thanks anyone that can help at this ungodly hour!
Original post by kingm
Any help on the following would be greatly received.. (I know it's late!)

(JAN 2010 AQA)

Q 7. b)

Screen Shot 2014-06-18 at 00.20.16.png

I don't understand how they go from the 1st line to the 2nd line in the mark scheme. I of course get the 'n' part, but not how they automatically get 3(2^n -1)

Thanks anyone that can help at this ungodly hour!

Spot the geometric progression.

For a GP with first term aa and common ratio rr, the sum of the first nn terms of the GP is given by a(rn1)r1\dfrac{a(r^n-1)}{r-1}.
Original post by kingm
...


Consider r=1n2r1 \displaystyle \sum_{r=1}^n 2^{r-1}

This is a well-recognised series.

Hope this helps. :smile:

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