A company’s net cash flow in year nnn, denoted by PnP_nPn (in millions of dollars), follows a geometric progression with common ratio rrr.
You are given that:
Show that r r\,r satisfies the equation r2−2r−2=0r^2 - 2r - 2 = 0r2−2r−2=0.
Given that the sum of the cash flows over an infinite time period, ∑n=1∞Pn\sum_{n=1}^{\infty} P_n∑n=1∞Pn, is convergent,
find the exact value of P1P_1P1.
Hence, calculate the exact value of S∞S_\inftyS∞.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
