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Part A Here are three attempted statements of a theorem which was provided in the video (it is also Example 2.5.1 in DMOI). None of these statements are correct. For each one, explain which piece is incorrect, why it matters, and how to fix it. "Theorem 1": For all integers n E Z, "Theorem 2": For all natural numbers n > 1, "Theorem 3": For all natural numbers n > 1, i=0 i=0 n i=0 i n(n + 1) 2 i(i+1) 2 n(n-1) 2

Part A Here are three attempted statements of a theorem which was provided in the video (it is also Example 2.5.1 in DMOI). None of these statements are correct. For each one, explain which piece is incorrect, why it matters, and how to fix it. "Theorem 1": For all integers n E Z, "Theorem 2": For all natural numbers n > 1, "Theorem 3": For all natural numbers n > 1, i=0 i=0 n i=0 i n(n + 1) 2 i(i+1) 2 n(n-1) 2

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 9TFE: Label each of the following statements as either true or false. Every decimal representation of a...
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Part A Here are three attempted statements of a theorem which was provided in the video (it is also Example 2.5.1 in DMOI). None of these statements are correct. For each one, explain which piece is incorrect, why it matters, and how to fix it. "Theorem 1": For all integers n = Z, "Theorem 2": For all natural numbers n ≥ 1, "Theorem 3": For all natural numbers n ≥ 1, n i=0 n i=0 = n Σi= i=0 n(n +1) 2 i(i+1) 2 n(n − 1) 2
Transcribed Image Text:Part A Here are three attempted statements of a theorem which was provided in the video (it is also Example 2.5.1 in DMOI). None of these statements are correct. For each one, explain which piece is incorrect, why it matters, and how to fix it. "Theorem 1": For all integers n = Z, "Theorem 2": For all natural numbers n ≥ 1, "Theorem 3": For all natural numbers n ≥ 1, n i=0 n i=0 = n Σi= i=0 n(n +1) 2 i(i+1) 2 n(n − 1) 2
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