CO Start with the geometric series Σχ. m=0 (a) Find the sum of the series Σ - = 1 (b) Find the sum of each of the following series. (1) Σ' πχ, |x| < 1 00 --- (ii) Π πχ -1, |x| < 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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Start with the geometric series 
 
 
n = 0
xn.

(a)

Find the sum of the series 
 
 
n = 1
nxn − 1,    |x| < 1.
 
 
 

(b)

Find the sum of each of the following series.
(i)
 
 
n = 1
nxn,    |x| < 1
 
 
 
(ii)
n
8n
 
n = 1
 
 
 

(c)

Find the sum of each of the following series.
(i)
 
 
n = 2
n(n − 1)xn,    |x| < 1
 
 
 
(ii)
n2 − n
2n
 
n = 2
 
 
 
(iii)
n2
2n
 
n = 1
00
Start with the geometric series X².
n = 0
(a) Find the sum of the series
n = 1
(b) Find the sum of each of the following series.
00
(1) Σ nx", lx| < 1
n = 1
8
n = 1
(c) Find the sum of each of the following series.
(1)
n(n-1)x", x < 1
n² - n
20
(ii)
n = 2
00
(ii) Σ
n = 2
(iii)
SW
n=1
n
N
nx-1, x < 1.
nx² -1,
Transcribed Image Text:00 Start with the geometric series X². n = 0 (a) Find the sum of the series n = 1 (b) Find the sum of each of the following series. 00 (1) Σ nx", lx| < 1 n = 1 8 n = 1 (c) Find the sum of each of the following series. (1) n(n-1)x", x < 1 n² - n 20 (ii) n = 2 00 (ii) Σ n = 2 (iii) SW n=1 n N nx-1, x < 1. nx² -1,
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ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage