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Chapter 9: Problem 58
Sum of a Finite Geometric Sequence, find the sum of the finite geometric sequence. $$ \sum_{n=1}^{8} 5\left(-\frac{5}{2}\right)^{n-1} $$
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Determine whether the statement is true or false. Justify your answer. Rolling a number less than 3 on a normal six-sided die has a probability of \(\frac{1}{3}\) . The complement of this event is to roll a number greater than \(3,\) and its probability is \(\frac{1}{2}\) .
Expanding a Complex Number In Exercises \(73-78\) , use the Binomial Theorem to expand the complex number. Simplify your result. $$(5-\sqrt{3} i)^{4}$$
Proving a Property In Exercises \(31-40,\) use mathematical induction to prove the property for all positive integers \(n .\) $$\text{ A }{\text factor}\text{ of }\left(n^{4}-n+4\right) \text { is } 2$$
Approximation In Exercises \(79-82,\) use the Binomial Theorem to approximate the quantity accurate to three decimal places. For example, in Exercise \(79,\) use the expansion \((1.02)^{8}=(1+0.02)^{8}\) $$=1+8(0.02)+28(0.02)^{2}+\cdots+(0.02)^{8}$$ $$(1.98)^{9}$$
Finding a Sum In Exercises \(45-54\) , find the sum using the formulas for the sums of powers of integers. $$\sum_{n=1}^{10} n^{3}$$
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