EXAMPLE 10 Discuss the convergence n! SOLUTION We observe that n (n-1) 3.2.1. ... an ² of the sequence Then, since 1/n → 0 theorem) ano. n. (n-1). n n. (n-1) n. n . . as 2 ... an n - 3.2.1 • n • n •n 3 an since the numerator is less than or equal to the denominator for the quantity in parenthesis. Therefore • n (1 -). ÷ n n!/n", where ² n we have (by the squeeze )
EXAMPLE 10 Discuss the convergence n! SOLUTION We observe that n (n-1) 3.2.1. ... an ² of the sequence Then, since 1/n → 0 theorem) ano. n. (n-1). n n. (n-1) n. n . . as 2 ... an n - 3.2.1 • n • n •n 3 an since the numerator is less than or equal to the denominator for the quantity in parenthesis. Therefore • n (1 -). ÷ n n!/n", where ² n we have (by the squeeze )
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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can you please explain this to me
Transcribed Image Text:EXAMPLE 10
Discuss the
n!
SOLUTION
We observe that
convergence
n (n-1) - 3.2.1.
an
=
of the sequence
n. (n-1).
Then, since
1/n → 0
theorem) ano.
n. (n-1).
n
² n
O
as
♦
2
.
an
since the numerator is less than or equal to the denominator
for the quantity in parenthesis. Therefore
3.2.1
n.n.n
an
3.2
-) = /1
n
• n • n
n→D,
n!/n", where
² n
we have (by the squeeze
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