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
Use an algebraic method to find the least value of 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
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.