Q. 13 Define what it means for a seque... [FREE SOLUTION]

Chapter 7: Q. 13 (page 591)

Define what it means for a sequence $\{a_{k}\}$ to be eventually strictly decreasing.

Short Answer

Expert verified

The sequence $\{a_{k}\}$ is eventually strictly decreasing sequence, if it is decreasing after some index $k$ , where $k 鈭� 鈩�$ .

Step by step solution

Step 1. Given information

The given sequence is, $\{a_{k}\}$ .

Step 2. Let ℕ>0.

The sequence $\{a_{k}\}$ is eventually strictly decreasing sequence, if it is decreasing after some index $k$ , where $k 鈭� 鈩�$ .

Let $\{a_{k}\}$ be the sequence and $鈩� > 0$ be such that for all $k > 鈩�, a_{k + 1} < a_{k}$ , then the sequence is eventually strictly decreasing sequence.

Step 3. Consider the sequence n-n2n=1∞

The terms of the sequence can be found by substituting $n = 1, 2, 3, . . .$

Hence, the terms of the sequence are, $1 - 1^{2}, 2 - 2^{2}, 3 - 3^{2}, . . . . . .$

The terms of the sequence are, $0, - 2, - 6$ .

The sequence is eventually strictly decreasing sequence as $a_{2} < a_{1}, a_{3} < a_{2}, . . . . ., a_{k + 1} < a_{k}$ .

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91影视

Define what it means for a sequence $\{a_{k}\}$ to be eventually strictly decreasing.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Let ℕ>0.

Step 3. Consider the sequence n-n2n=1∞

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91影视

Define what it means for a sequence akto be eventually strictly decreasing.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Let ℕ>0.

Step 3. Consider the sequence n-n2n=1∞

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Logic and Functions

Mechanics Maths

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Define what it means for a sequence $\{a_{k}\}$ to be eventually strictly decreasing.