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Chapter 14: Problem 34
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$5+5^{2}+5^{3}+\dots+5^{12}$$
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Use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 69 and 70 to verify the expansion. $$f_{1}(x)=(x+2)^{6}$$
Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. $$-1,1,-1,1, \dots$$
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. In order to expand \(\left(x^{3}-y^{4}\right)^{5},\) I find it helpful to rewrite the expression inside the parentheses as \(x^{3}+\left(-y^{4}\right)\).
Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. $$1 \cdot 3,2 \cdot 4,3 \cdot 5,4 \cdot 6, \dots$$
Use the formula for the value of an annuity to solve Exercises. Round answers to the nearest dollar. To save money for a sabbatical to earn a master's degree, you deposit \(\$ 2500\) at the end of each year in an annuity that pays \(6.25 \%\) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.
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