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Chapter 7: Q. 35 (page 592)

In Exercises 31鈥�36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
$\{\frac{\sqrt{k}}{k}\}$

Short Answer

Expert verified

The first five terms of the sequence are $1, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}}, \frac{1}{2}, \frac{1}{\sqrt{5}} .$

Step by step solution

01

Step 1. Given information.

The given sequence is $\{\frac{\sqrt{k}}{k}\}$ .

02

Step 2. First term.

The general sequence is $a_{k} = \frac{\sqrt{k}}{k}$ .

For the first term, $k = 1,$

$a_{1} = \frac{\sqrt{1}}{1} = 1$

03

Step 3. Remaining Terms.

Now, put

$k = 2, a_{2} = \frac{\sqrt{2}}{2} a_{2} = \frac{1}{\sqrt{2}} k = 3, a_{3} = \frac{\sqrt{3}}{3} a_{3} = \frac{1}{\sqrt{3}} k = 4, a_{4} = \frac{\sqrt{4}}{4} = \frac{1}{2} k = 5, a_{5} = \frac{\sqrt{5}}{5} a_{5} = \frac{1}{\sqrt{5}}$

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Most popular questions from this chapter

Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.

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