# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#2

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**Question**

The common ratio of a geometric progression is r. The first term of the progression is and the sum to infinity is S.

** i. **Show that S = 2 − r.

** ii. **Find the set of possible values that S can take.

**Solution**

** i.
**

From the given information, we can compile following data about Geometric Progression (G.P);

Expression for the sum to infinity of the Geometric Progression (G.P) when or ;

Therefore for the given case;

** ii.
**

We have found that;

Expression for the sum to infinity of the Geometric Progression (G.P) when or ;

Therefore;

We have found in (i) that , therefore;

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