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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 2. (page 836)

$(\begin{matrix} n \\ 0 \end{matrix}) = 鈥� 鈥�$ and $(\begin{matrix} n \\ 1 \end{matrix}) = 鈥� 鈥�$

Short Answer

Expert verified

The value of $(\begin{matrix} n \\ 0 \end{matrix}) = 1$ and $(\begin{matrix} n \\ 1 \end{matrix}) = n$

Step by step solution

01

Step 1. Explaining first part

$鈬� (\begin{matrix} n \\ 0 \end{matrix}) = \frac{n!}{0! (n - 0)!}$

$鈬� (\begin{matrix} n \\ 0 \end{matrix}) = \frac{n!}{n!} = 1$

02

Step 2. Explaining second part

$鈬� (\begin{matrix} n \\ 1 \end{matrix}) = \frac{n!}{1! (n - 1)!}$

$鈬� (\begin{matrix} n \\ 1 \end{matrix}) = \frac{n (n - 1)!}{(n - 1)!} = n$

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Most popular questions from this chapter

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = 1; a_{n} = n - a_{n - 1}$

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$8 + 4 + 2 + . . . .$

In Problems 71-82, find the sum of each sequence.

${鈭�}_{k = 8}^{40} (- 3 k)$

How much do you need to invest now at $5 %$ per annum compounded monthly so that in 1 year you will have $$ 10000$ ?

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$

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