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Magazine Problem 18
Determine if the given sequence is arithmetic, geometric or neither. If it is arithmetic, find the common difference \(d ;\) if it is geometric, find the common ratio \(r\). \(17,5,-7,-19, \ldots\)
Problem 19
In Exercises \(18-22,\) use the Binomial Theorem to find the indicated term. The term containing \(x^{117}\) in the expansion \((x+2)^{118}\)
Problem 20
Use the formulas in Equation 9.2 to find the sum. $$ \sum_{n=1}^{10}\left(\frac{1}{2}\right)^{n} $$
Problem 20
In Exercises \(18-22,\) use the Binomial Theorem to find the indicated term. The term containing \(x^{\frac{7}{2}}\) in the expansion \((\sqrt{x}-3)^{8}\)
Problem 20
Determine if the given sequence is arithmetic, geometric or neither. If it is arithmetic, find the common difference \(d ;\) if it is geometric, find the common ratio \(r\). \(0.9,9,90,900, \ldots\)
Problem 21
In Exercises \(18-22,\) use the Binomial Theorem to find the indicated term. The term containing \(x^{-7}\) in the expansion \(\left(2 x-x^{-3}\right)^{5}\)
Problem 21
Determine if the given sequence is arithmetic, geometric or neither. If it is arithmetic, find the common difference \(d ;\) if it is geometric, find the common ratio \(r\). \(a_{n}=\frac{n !}{2}, n \geq 0\)
Problem 22
In Exercises \(18-22,\) use the Binomial Theorem to find the indicated term. The constant term in the expansion \(\left(x+x^{-1}\right)^{8}\)
Problem 22
In Exercises \(22-30,\) find an explicit formula for the \(n^{\text {th }}\) term of the given sequence. Use the formulas in Equation 9.1 as needed. \(3,5,7,9, \ldots\)
Problem 22
Use the formulas in Equation 9.2 to find the sum. $$ \sum_{k=0}^{5} 2\left(\frac{1}{4}\right)^{k} $$
