Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.2 - Arithmetic Sequences - 12.2 Exercises - Page 857: 68



Work Step by Step

Applying the rule for multiplying powers with the same base, $10^{a_{1}}\cdot 10^{a_{2}}\cdot....\cdot 10^{a_{n}}=10^{a_{1}+a_{2}+...+a_{n}}$ On the RHS, the exponent is the sum of the sequence $0.1, 0.2, 0.3, ... , 1.9,$ which has a common differrence $d=0.1$, so, it is arithmetic, with first and last terms $a=0.1$ and $a_{19}=1.9.$ $S_{n}=n(\displaystyle \frac{a+a_{n}}{2})$ $S_{19}= 19(\displaystyle \frac{0.1+1.9}{2})=19$ Thus, the product equals $ 10^{19}$
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