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Sum of a Geometric Series Proof

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Sum of a Geometric Series Proof

Juneau

I am pretty certain you need to know this for C2 (edexcel at aleast) so does anyone know a goodproof for the sum of a geometric series please?

Reply 1

Dimez

Sn= a + ar + ar² + ............... ar^(n-1) (1)
Multiply by r

Snr=ar + ar² + ar³+.................+ ar^n (2)

(1) - (2) ==> Sn - Snr= a - ar^n
Sn(1 - r)=a(1-r^n)
Sn= a(1 - r^n) / 1 -r

Reply 2

Seth

First start with your expression for the sum of the geometric series, then multiply both sides by r:
Sn=a+ar+ar²+ar³+.........ar^(n-2)+ar^(n-1)

rSn = ar+ar²+ar³+ar^4..............+ar^(n-1)+ar^n

Now if you subtact rSn from Sn:

Sn-rSn=a-ar^n
Sn(1-r)=a(1-ar^n)
Sn = a(1-ar^n)/(1-r)

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