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Problem: Assume (n) is a sequence of reals, and I is a real number. Are the following statements true or false (and prove you answers): 1. If (₂)→ 1 and 1> 0 then there exists an N and a p > 0 such that for all n ≥ N, n > p 2. If (n) → 1 and 2 > 0 then there exists an N such that for all n > N, xn ≥ 0

Problem: Assume (n) is a sequence of reals, and I is a real number. Are the following statements true or false (and prove you answers): 1. If (₂)→ 1 and 1> 0 then there exists an N and a p > 0 such that for all n ≥ N, n > p 2. If (n) → 1 and 2 > 0 then there exists an N such that for all n > N, xn ≥ 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part 1 and 2 please.

Problem: Assume (n) is a sequence of reals, and is a real number. Are the following statements true or false (and prove you answers): 1. If (n) → 1 and 2 > 0 then there exists an N and a p > 0 such that for all n > N₁ xn > p 2. If (In) → 1 and 1> 0 then there exists an N such that for all n ≥ N, xn ≥ 0
Transcribed Image Text:Problem: Assume (n) is a sequence of reals, and is a real number. Are the following statements true or false (and prove you answers): 1. If (n) → 1 and 2 > 0 then there exists an N and a p > 0 such that for all n > N₁ xn > p 2. If (In) → 1 and 1> 0 then there exists an N such that for all n ≥ N, xn ≥ 0
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