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)308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.