Chapter 7: Q, 36 (page 592)

In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index $1$ .
$\{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{k}}\}$

Short Answer

Expert verified

The first five terms are $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32} .$

Step by step solution

Step 1. Given information.

The given sequence is $\{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{k}}\}$ .

Step 2. First term.

The general term of the sequence is $a_{k} = \frac{1}{2^{k}} .$

For first term, $k = 1,$

$a_{1} = \frac{1}{2^{1}}$

Step 3. Remaining terms.

Now, when,

$k = 2, a_{2} = \frac{1}{2^{2}} = \frac{1}{4} k = 3, a_{3} = \frac{1}{2^{3}} = \frac{1}{8} k = 4, a_{4} = \frac{1}{2^{4}} = \frac{1}{16} k = 5, a_{5} = \frac{1}{2^{5}} = \frac{1}{32}$

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In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index $1$ .
$\{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{k}}\}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First term.

Step 3. Remaining terms.

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In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.12+14+18+⋯+12k

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First term.

Step 3. Remaining terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Calculus

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index $1$ .
$\{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{k}}\}$