Show that
∑r=112(3r+7+2r)=8508\sum_{r=1}^{12} \left(3r + 7 + 2^r\right) = 8508∑r=112(3r+7+2r)=8508
A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by
u1=25\displaystyle u_1 = \frac{2}{5}u1=52, un+1=1un\displaystyle u_{n+1} = \frac{1}{u_n}un+1=un1
Find the exact value of ∑r=1100ur\sum_{r=1}^{100} u_r∑r=1100ur.
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.