College Algebra 7th Edition

Published by Brooks Cole

Chapter 8, Sequences and Series - Chapter 8 Review - Exercises - Page 639: 8

Answer

$a_1=1$ $\displaystyle a_2=\frac{1}{2}$ $\displaystyle a_3=\frac{1}{6}$ $\displaystyle a_4=\frac{1}{24}$ $\displaystyle a_5=\frac{1}{120}$ $\displaystyle a_6=\frac{1}{720}$ $\displaystyle a_7=\frac{1}{5040}$

Work Step by Step

We are given: $\displaystyle a_{n}= \frac{a_{n-1}}{n}$ and $a_1=1$ We evaluate: $a_1=1$ $\displaystyle a_2=\frac{a_{1}}{2}=\frac{1}{2}$ $\displaystyle a_3=\frac{a_{2}}{3}=\frac{1}{2*3}=\frac{1}{6}$ $\displaystyle a_4=\frac{a_{3}}{4}=\frac{1}{6*4}=\frac{1}{24}$ $\displaystyle a_5=\frac{a_{4}}{5}=\frac{1}{24*5}=\frac{1}{120}$ $\displaystyle a_6=\frac{a_{5}}{6}=\frac{1}{120*6}=\frac{1}{720}$ $\displaystyle a_7=\frac{a_{6}}{7}=\frac{1}{720*7}=\frac{1}{5040}$

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