Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 537: 4

Answer

\begin{array}{lclcl} b_1=1&\\ b_2=3&\\ b_3=20&\\ b_4=210\\ \end{array}

Work Step by Step

Given $$ b_{n}=\frac{(2 n-1) !}{n !}, \ \ \ \ \ \ n= 1,2,3, \dots $$ So, we get \begin{array}{|l|l|}\hline & n& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b_n \\ \\ \hline \text{First Term} & 1 & b_1= \frac{(2 \times 1-1) !}{1 !}=\frac{1 !}{1}=1 \\ \\ \hline \text{Second Term} & 2 & b_2=\frac{(2 \times 2-1) !}{2 !}=\frac{3 !}{2 !}=\frac{3 \times2 !}{2 !}=3 \\ \\ \hline \text{Third Term} & 3 & b_3= \frac{(2 \times 3-1) !}{3 !}=\frac{5 !}{3 !}=\frac{5 \times 4 \times 3 !}{3 !}=20 \\ \\ \hline \text{Fourth Term} & 4 & b_4= \frac{(2 \times 4-1) !}{4 !}=\frac{7 !}{4 !}=\frac{7 \times 6 \times \ 5 \times 4 !}{4 !}=210\\ \\ \hline \end{array}
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