A geometric progression has first term u1 u_1\,u1 and common ratio kkk.
Show that the sum of the first n n\,n terms of this progression, SnS_nSn, can be expressed as
Sn=u1(1−kn)1−k S_n = \frac{u_1(1 - k^n)}{1 - k} Sn=1−ku1(1−kn)Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 100 questions 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, 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.