Result 14.6 ( ₁² + ²) = lim = ∞0. Proof Let M be a positive number. Choose N = √M and let n be any integer such that 1 n> N. Hence, n > √M and so n²> M. Thus n² + n >n² > M.
Result 14.6 ( ₁² + ²) = lim = ∞0. Proof Let M be a positive number. Choose N = √M and let n be any integer such that 1 n> N. Hence, n > √M and so n²> M. Thus n² + n >n² > M.
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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Question
Please explain the following proof in more detail, i dont get where the M comes from and what the intutian comes from
![Result 14.6
(n² + 1² ) = ∞0.
lim n²
Proof Let M be a positive number. Choose N = √M
and let n be any integer such that
1
n > N. Hence, n > √M and so n²> M. Thus n² +
>n² > M.
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e237d3f-b8e6-4775-a6f9-5671b153aef2%2Fc05b896b-0007-4f7e-af2b-dd7c5e5f6f8a%2Fk34dlae_processed.png&w=3840&q=75)
Transcribed Image Text:Result 14.6
(n² + 1² ) = ∞0.
lim n²
Proof Let M be a positive number. Choose N = √M
and let n be any integer such that
1
n > N. Hence, n > √M and so n²> M. Thus n² +
>n² > M.
n
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