Analysis and Approaches SL — Questionbank

All Concepts - Functions

All questions in Topic 2 Functions

Question 9

NO CALCULATOR

Spicy

[Maximum mark: 12]

Consider the series

\ln x + q\, lnx + \frac{1}{4}\ln x + \ldots,

where $x \in R, x > 1, q \in R, q \neq 0$


(a.i) Show that if the series is geometric then $q = \ \pm \frac{1}{2}$	[2]
(a.ii) Given that q > 0, and S_∞ = 4 + 4, find the value of x Now consider the case where the series is arithmetic with common difference d.	[3]
(b.i) Show that in this case $q = \ \frac{5}{8}$	[3]
(b.ii) Write down d in the form mln x, where m ∈ Q	[1]
(b.iii) Suppose the sum of the first n terms of the series equals $- \frac{7}{8}\ln x$ . Find the value of n.	[3]