a Show that a GP has a limiting sum if 0 < 1 – r < 2. b By calculating the common ratio, show that there is no GP with first term 8 and limiting sum 2. C A GP has positive first term a, and has a limiting sum Sm. Show that S, > }a. d Find the range of values of the limiting sum of a GP with: i a = 6 16 ii a = -8 iv a < 0 iii a > 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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a Show that a GP has a limiting sum if 0 < 1 – r < 2.
b By calculating the common ratio, show that there is no GP with first term 8 and limiting sum 2.
C A GP has positive first term a, and has a limiting sum Sm. Show that S, > }a.
d Find the range of values of the limiting sum of a GP with:
i a = 6
16
ii a = -8
iv a < 0
iii a > 0
Transcribed Image Text:a Show that a GP has a limiting sum if 0 < 1 – r < 2. b By calculating the common ratio, show that there is no GP with first term 8 and limiting sum 2. C A GP has positive first term a, and has a limiting sum Sm. Show that S, > }a. d Find the range of values of the limiting sum of a GP with: i a = 6 16 ii a = -8 iv a < 0 iii a > 0
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