Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.1 - Sequences - 11.1 Exercises - Page 704: 19

Answer

0.4286, 0.4615, 0.4737, 0.4800, 0.4839, 0.4865, 0.4884, 0.4898, 0.4909, 0.4918 $\lim\limits_{n \to \infty}=\frac{1}{2}$

Work Step by Step

Because the highest power of n is 1, we divide both the numerator and denominator by n to the power of 1. This will allow us to end up with $\frac{\frac{3n}{n}}{\frac{1}{n}+\frac{6}{n}}$. Simplifying it to $\frac{3}{\frac{1}{n}+6}$ will allow us to find the limit of the sequence. $\lim\limits_{n \to \infty} a_{n}= \frac{1}{2}$ To find the first 10 terms of the sequence, we will plug in values of a from 1 to 10.
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