Define a digit to be an element of the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) 00 00 Show that Σ n=1 10 = Σ n=1 - if and only if one of the following two conditions holds: 10 Either (i) a = b for every n or 12 (ii) there is some N&N U (0) such that • a = b_ for 1 ≤ n ≤N, a = b + 1, and a = 0 and b = 9 for all n > N.
Define a digit to be an element of the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) 00 00 Show that Σ n=1 10 = Σ n=1 - if and only if one of the following two conditions holds: 10 Either (i) a = b for every n or 12 (ii) there is some N&N U (0) such that • a = b_ for 1 ≤ n ≤N, a = b + 1, and a = 0 and b = 9 for all n > N.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 56E
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Transcribed Image Text:Define a digit to be an element of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
00
00
Show that Σ
n=1
10"
= Σ
n
n=1
b
- if and only if one of the following two conditions holds:
10"
Either (i) a = b_for every n or
12
(ii) there is some N&N U {0} such that
a
= b for 1 ≤ n ≤ N,
12
a = b₁ + 1, and
N
a = 0 and b = 9 for all n > N.
12
12
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