## Calculus, 10th Edition (Anton)

Published by Wiley

# Chapter 9 - Infinite Series - 9.1 Sequences - Exercises Set 9.1 - Page 605: 10

#### Answer

first five terms: $1, -ln(2), -ln(3), -ln(4), -ln(5)$, diverges

#### Work Step by Step

To find the first five terms of the sequence, put the values $1,2,3,4,5$ into the function $a_n=ln(\frac{1}{n})$. To find if the sequence converges, find the limit as n approaches positive infinity. This leaves $$\lim\limits_{n \to \infty} ln(\frac{1}{n})$$ Since $\frac{1}{n}$ is equal to $n^{-1}$, using logarithm rules, the limit can get changed into $$\lim\limits_{n \to \infty} -ln(n)$$ The limit approaches negative infinity as n approaches infinity. Therefore, the sequence diverges.

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