Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 9 - Infinite Series - 9.1 Sequences - Exercises Set 9.1: 7

Answer

first five terms: $\frac{1}{3}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{5}{7}$, converges to 1

Work Step by Step

To find the first five terms of the sequence, put the values $1,2,3,4,5$ into the function $a_n=\frac{n}{n+2}$. To find if the sequence converges, find the limit as n approaches positive infinity. This leaves $$\lim\limits_{n \to \infty} \frac{n}{n+2}$$ Since the highest degree polynomial in the numerator and denominator match, the coefficients of those highest degree polynomials is the limit. In this case, it is $\frac{1}{1}=1$.
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