   Chapter 11.1, Problem 33E

Chapter
Section
Textbook Problem

# Determine whether the sequence converges or diverges. If it converges, find the limit.33. a n = n 2 n 3 + 4 n

To determine

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

Explanation

Given:

The sequence is an=n2n3+4n .

Definition used:

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

Laws of limits for sequences used:

If f(x) and g(x) are two functions, then limxa[f(x)g(x)]=limxaf(x)limxag(x) and limxag(x)0 .

Calculation:

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

Compute limnn2n3+4n .

Divide the numerator and the denominator by the highest power.

limnn2n3+4n=limnn2n3n3+4nn3=limn∞</

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