Chapter 7: Q. 25 (page 592)

In Exercises, find a plausible formula for the general term of the given sequence.
$\{0, 1, 0, 1, 0, 1, \dots\}$

Short Answer

Expert verified

The plausible formula for the general term of the sequence is $a_{k} = \frac{1}{2} [1 + {(- 1)}^{k}] .$

Step by step solution

Step 1. Given information.

The given sequence is $\{0, 1, 0, 1, 0, 1, \dots\} .$

Step 2. plausible formula for the general term.

the sequence $\{0, 1, 0, 1, 0, 1, \dots\}$ has $0 & 1$ alternately.

the sequence can be written as follows.

role="math" localid="1649186161903" ${\{\frac{1}{2} [1 + {(- 1)}^{k}]\}}_{k = 1}^{\infty} = \{0, 1, 0, 1, 0, 1, \dots\}$

where for every odd value of k,the term will be zero

For every even value ofk,the term will be one.

So plausible formula for the general term of the sequence is role="math" localid="1649186184028" $a_{k} = \frac{1}{2} [1 + {(- 1)}^{k}]$

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In Exercises, find a plausible formula for the general term of the given sequence.
$\{0, 1, 0, 1, 0, 1, \dots\}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. plausible formula for the general term.

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In Exercises, find a plausible formula for the general term of the given sequence.0,1,0,1,0,1,…

Short Answer

Step by step solution

Step 1. Given information.

Step 2. plausible formula for the general term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Geometry

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises, find a plausible formula for the general term of the given sequence.
$\{0, 1, 0, 1, 0, 1, \dots\}$