Consider the finite geometric series defined by the summation ∑i=0n−1ARi\sum_{i=0}^{n-1} A R^i∑i=0n−1ARi, where R≠1R \neq 1R=1.
Prove that the sum Sn S_n\,Sn of this series is given by the formula
Sn=A(1−Rn)1−R S_n = \frac{A(1 - R^n)}{1 - R} Sn=1−RA(1−Rn)38 exam-style questions on AQA A Level Maths 1.7.5 Geometric sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.