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Chapter 14: Problem 5
Evaluate the given binomial coefficient. $$\left(\begin{array}{l}6 \\\6\end{array}\right)$$
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Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.
Will help you prepare for the material covered in the next section. Consider the sequence \(8,3,-2,-7,-12, \ldots .\) Find \(a_{2}-a_{1}, a_{3}-a_{2}, a_{4}-a_{3},\) and \(a_{5}-a_{4} .\) What do you observe?
Will help you prepare for the material covered in the next section. Use the formula \(a_{n}=4+(n-1)(-7)\) to find the eighth term of the sequence \(4,-3,-10, \ldots\)
Expand and write the answer as a single logarithm with a coefficient of 1. $$\sum_{i=1}^{4} \log (2 i)$$
Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. $$\begin{aligned}&f_{1}(x)=(x+1)^{4} & f_{2}(x)=x^{4}\\\&f_{3}(x)=x^{4}+4 x^{3} & f_{4}(x)=x^{4}+4 x^{3}+6 x^{2}\\\&f_{5}(x)=x^{4}+4 x^{3}+6 x^{2}+4 x\\\&f_{6}(x)=x^{4}+4 x^{3}+6 x^{2}+4 x+1\end{aligned}$$ Use a \([-5,5,1]\) by \([-30,30,10]\) viewing rectangle.
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