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.

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Chapter2: Second-order Linear Odes
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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
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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