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Chapter 7: Q. 31 (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.
$\{\frac{1 - (- 1)^{k}}{k}\}$

Short Answer

Expert verified

The first five terms are $2, 0, \frac{2}{3}, 0, \frac{2}{5}$ .

Step by step solution

01

Step 1. Given information.

The given sequence is $\{\frac{1 - (- 1)^{k}}{k}\}$ .

02

Step 2. First term.

The generals sequence will be,

$a_{k} = \frac{1 - (- 1)^{k}}{k} k = 1, a_{1} = \frac{1 - (- 1)}{k} = 2$

03

Step 3. Remaining terms.

Now put,

$k = 2, a_{2} = \frac{1 - (- 1)^{2}}{k} = 0 k = 3, a_{3} = \frac{1 - (- 1)^{3}}{3} = \frac{2}{3} k = 4, a_{4} = \frac{1 - (- 1)^{4}}{4} = 0 k = 5, a_{5} = \frac{1 - (- 1)^{5}}{5} = \frac{2}{5}$

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