Consider the sequences (an) and (bn) in R given by (¹ + 1)", an = 1 ₁ bn = Σ₁-05! Vn EN. j=0 Recall that (an), (bn) are strictly increasing, and limn→∞ an = mine limn→∞ n(e — an) as well as limn→∞ n!n(e — bn). - limn→∞ bn = e. Deter-

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the sequences (an) and (bn) in R given by
(1 + ²)", b₁ = Σ² - 03/1
bn
j=0 j!
n
an =
Vn EN.
=
Recall that (an), (bn) are strictly increasing, and limn→∞ an
mine limn→∞ n(e – an) as well as limn→∞ n!n(e — bn).
limn→∞ bn
= e. Deter-
Transcribed Image Text:Consider the sequences (an) and (bn) in R given by (1 + ²)", b₁ = Σ² - 03/1 bn j=0 j! n an = Vn EN. = Recall that (an), (bn) are strictly increasing, and limn→∞ an mine limn→∞ n(e – an) as well as limn→∞ n!n(e — bn). limn→∞ bn = e. Deter-
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