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 Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 100 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, matched to the Edexcel A Level Maths (9MA0) 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.