A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by un=20×0.85nu_n = 20 \times 0.85^nun=20×0.85n.
State the first term and common ratio of the geometric series.
Use an algebraic method to find the least possible value for N N\,N for which ∑n=1∞un−∑n=1Nun<1\sum_{n=1}^{\infty} u_n - \sum_{n=1}^N u_n < 1∑n=1∞un−∑n=1Nun<1.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, 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. Each one has a worked solution and a mark scheme showing where the marks go.