College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 68

Answer

$P=10^{19}$

Work Step by Step

We are asked to find the product: $P=10^{1/10}\cdot 10^{2/10}\cdot 10^{3/10}\cdot 10^{4/10}... 10^{19/10}$ We simplify the powers: $10^{(1+2+3+4+...+19)/10}$ We see that we have an arithmetic sequence with $a=1$ and $a_{19}=19$. We find the partial sum: $S_{19}=\frac{19}{2}(1+19)=19*20/2=19*10=190$ Thus the product is: $P=10^{190/10}=10^{19}$
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