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Chapter 10: Problem 23
Find the sum of the convergent series. $$ 1+0.1+0.01+0.001+\cdots $$
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Compound Interest Consider the sequence \(\left\\{A_{n}\right\\}\) whose \(n\) th term is given by \(A_{n}=P(1+r)^{n}\) where \(P\) is the principal, \(A_{n}\) is the amount of compound interest after \(n\) years, and \(r\) is the annual percentage rate. Write the first 10 terms of the sequence for \(P= 5000 \text{dollars}\) and \(r=0.08\)
Determine the convergence or divergence of the series. Use a symbolic algebra utility to verify your result. $$ \sum_{n=0}^{\infty} n ! $$
Cost A well-drilling company charges 25 dollars for drilling the first foot of a well, 25.10 dollars for drilling the second foot, 25.20 dollars for the third foot, and so on. Determine the cost of drilling a 100 -foot well.
Sales A company produces a new product for which it estimates the annual sales to be 8000 units. Suppose that in any given year \(10 \%\) of the units (regardless of age) will become inoperative. (a) How many units will be in use after \(n\) years? (b) Find the market stabilization level of the product.
Write an expression for the \(n\) th term of the sequence. (There is more than one correct answer.) $$ -2,2,-2,2, \dots $$
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