Chapter 7: Q. 5 (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, then
$(a_{k} + b_{k}) \to$

Short Answer

Expert verified

The required answer is $(a_{k} + b_{k}) \to L + M$

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

As sequences are also coined as functions, So, the properties of limits that applied for functions can also be applied to sequences.

Thus, $(a_{k} + b_{k}) \to L + M$

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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, then
$(a_{k} + b_{k}) \to$

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, thenak+bk→

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Most popular questions from this chapter

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Discrete Mathematics

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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, then
$(a_{k} + b_{k}) \to$