   Chapter 11.1, Problem 48E

Chapter
Section
Textbook Problem

# Determine whether the sequence converges or diverges. If it converges, find the limit.48. a n = n n

To determine

Whether the sequence converges or diverges and obtain the limit if the sequence converges.

Explanation

Given:

The sequence is an=nn .

Definition used:

If an is a sequence and limnan exists, then the sequence an is said to be converges; otherwise it diverges.

Calculation:

Obtain the limit of the sequence to investigate whether the sequence converges or diverges.

Compute limnan=limn(n1n) .

Apply the Exponent rule ax=exln(a) and simplify the expressions.

limn(n1n)=limn(e1nln(n))

=elimn(ln(n)n) (1)

Obtain the value of limn(ln(n)n) .

Since is in indeterminate form, apply the L’Hospital’s Rule

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