Chapter 7: Q. 7 (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
If M=0 then $\frac{a_{k}}{b_{k}} \to$

Short Answer

Expert verified

The required answer is $\frac{a_{k}}{b_{k}} \to \frac{L}{M}$

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, if M=0 then $\frac{a_{k}}{b_{k}} \to \frac{L}{M}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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
If M=0 then $\frac{a_{k}}{b_{k}} \to$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Logic and Functions

Applied Mathematics

Pure Maths

Decision Maths

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 akandbkareconvergentsequenceswithak→Landbk→Mask→∞and if c is any constant, then If M=0 thenakbk→

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Logic and Functions

Applied Mathematics

Pure Maths

Decision Maths

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
If M=0 then $\frac{a_{k}}{b_{k}} \to$