Chapter 7: Q. 11 (page 655)

Fill in the blanks to complete each of the following theorem statements.
Basic Limit Rules for Convergent Sequences: If $\{a_{k}\} and \{b_{k}\} are convergent sequences with a_{k} \to L and b_{k} \to M as k \to \infty$ and if c is any constant,
If $|a_{k}| \to_____, then a_{k} \to_____$

Short Answer

Expert verified

The required answer is $|a_{k}| \to 0, then a_{k} \to 0$

Step by step solution

Step 1. Given Information

The given data is if $\{a_{k}\} and \{b_{k}\} are convergent sequences with a_{k} \to L and b_{k} \to M as k \to \infty$

Step 2. Explanation

Using the concept of limit of absolute values of a sequence,

If $|a_{k}| \to 0, then a_{k} \to 0$

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Fill in the blanks to complete each of the following theorem statements.
Basic Limit Rules for Convergent Sequences: If $\{a_{k}\} and \{b_{k}\} are convergent sequences with a_{k} \to L and b_{k} \to M as k \to \infty$ and if c is any constant,
If $|a_{k}| \to_____, then a_{k} \to_____$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Fill in the blanks to complete each of the following theorem statements.Basic Limit Rules for Convergent Sequences: If akandbkareconvergentsequenceswithak→Landbk→Mask→∞and if c is any constant,Ifak→_____,thenak→_____

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements.
Basic Limit Rules for Convergent Sequences: If $\{a_{k}\} and \{b_{k}\} are convergent sequences with a_{k} \to L and b_{k} \to M as k \to \infty$ and if c is any constant,
If $|a_{k}| \to_____, then a_{k} \to_____$