   Chapter 11.2, Problem 15E

Chapter
Section
Textbook Problem

# Let a n = 2 n 3 n + 1 . (a) Determine whether {an} is convergent. (b) Determine whether ∑ n = 1 ∞ a n is convergent.

(a)

To determine

Whether the sequence is convergent or divergent.

Explanation

Given:

The sequence is an=2n3n+1 .

Definition used:

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

Calculation:

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

Compute the value of limnan=limn2n3n+1 .

Divide the numerator and the denominator by the highest power.

limn2n3n+1=limn2nn3n+1n=limn23nn<

(b)

To determine

Whether the series is convergent or divergent.

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