Show that ∑r=18(2r+4+2r)=614\sum_{r=1}^{8} (2r + 4 + 2^r) = 614∑r=18(2r+4+2r)=614.
A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by un+1=1un,u1=12\displaystyle u_{n+1} = \frac{1}{u_n}, u_1 = \frac{1}{2}un+1=un1,u1=21. Find the exact value of ∑r=1100ur\sum_{r=1}^{100} u_r∑r=1100ur.
324 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.