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If S is the sum to infinity of a G.P. whose first term is
then the sum of the first n terms is

Show answer and solution
S=91−γS = \frac{9}{1 - \gamma}
⇒r=1−a/3\Rightarrow r = 1 - a/3
Sn=a(1−rn)(1−r)=a(1−(1−a/s)n)1−(1−9/s)S_{n} = \frac{a\left( 1 - r^{n} \right)}{(1 - r)} = \frac{a\left( 1 - (1 - a/s)^{n} \right)}{1 - (1 - 9/s)}
=s(1−(1−a/s)n)= s\left( 1 - (1 - a/s)^{n} \right).

Source: Grass-G / M-06 Mathematics Paper 14 October.docx

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