   Chapter 11.1, Problem 85E

Chapter
Section
Textbook Problem

# (a) Use a graph to guess the value of the limit lim n → ∞ n 5 n ! (b) Use a graph of the sequence in part (a) to find the smallest values of N that correspond to ε = 0.1 and ε = 0.001 in Definition 2.

(a)

To determine

To guess: The value of the limit by using a graph.

Explanation

Given:

The sequence is an=n5n! . (1)

Calculation:

Obtain the first 15 terms of the sequence.

 n n5 n! an=n5n! 1 15=1 1!=1 151!=1.0000 2 25=32 2!=2 252!=16.0000 3 35=243 3!=6 353!=40.5000 4 45=1,024 4!=24 454!=42.6667 5 55=3,125 5!=120 555!=26.0417 6 65=7,776 6!=720 656!=10.8000 7 75=16,807 7!=5,040 757!=3.3347 8 85=32,768 8!=40,320 858!=0.8127 9 95=59,049 9!=362,880 959!=0

(b)

To determine

To find: The smallest values of N that correspond to ε=0.1 and ε=0.001 in Definition 2.

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