In a geometric sequence x1,x2,x3,…x_1, x_2, x_3, \dotsx1,x2,x3,…:
Show that r r\,r satisfies the equation 3r2−2r−2=03r^2 - 2r - 2 = 03r2−2r−2=0
Given that the geometric sequence has a sum to infinity,
find the exact value of x1 x_1\,x1 in the form a+b7a + b\sqrt{7}a+b7 where a,b∈Qa, b \in \mathbb{Q}a,b∈Q.
Hence, calculate the value of S∞S_\inftyS∞.
Practise Edexcel A Level Maths 3.4 Geometric Series with exam-style questions for A Level Maths. 27 questions, 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.