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Chapter 10: Problem 11
Determine the convergence or divergence of the \(p\)-series. $$ \sum_{n=1}^{\infty} \frac{1}{n^{4 / 3}} $$
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Verify that the infinite series diverges. $$ \sum_{n=0}^{\infty} 2(-1.03)^{n}=2-2.06+2.1218-\cdots $$
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.
Physical Science In a certain brand of CD player, after the STOP function is activated, the disc, during each second after the first second, makes \(85 \%\) fewer revolutions than it made during the preceding second. In coming to rest, how many revolutions does the disc make if it makes 5.5 revolutions during the first second after the STOP function is activated?
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.
Determine the convergence or divergence of the series. Use a symbolic algebra utility to verify your result. $$ \sum_{n=1}^{\infty} \frac{n+10}{10 n+1} $$
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