A geometric series is a+ar+ar2+…a + ar + ar^2 + \dotsa+ar+ar2+…
Prove that the sum of the first n n\,n terms of this series is given by
Sn=a(1−rn)1−r. S_n = \frac{a(1 - r^n)}{1 - r}. Sn=1−ra(1−rn).Find
∑k=110100(2k). \sum_{k=1}^{10} 100(2^k). k=1∑10100(2k).Find the sum to infinity of the geometric series
56+518+554+… \frac{5}{6} + \frac{5}{18} + \frac{5}{54} + \dots 65+185+545+…State the condition for an infinite geometric series with common ratio r r\,r to be convergent.
9 exam-style questions on Edexcel A Level Old Maths Sequences and Series. Each one has a worked solution and a mark scheme showing where the marks go.