Question

Fill in the blanks to complete each of the following theorem statements.

Basic Limit Rules for Convergent Sequences: If $\left\{a_k\right\}\mathrm{and}\left\{b_k\right\}\mathrm{are}\mathrm{convergent}\mathrm{sequences}\mathrm{with}{a}_k\to L\mathrm{and}{b}_k\to M\mathrm{as}k\to \infty$and if c is any constant, then

If M=0 then$\frac{a_k}{b_k}\to$

Short answer

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 $\left\{a_k\right\}\mathrm{and}\left\{b_k\right\}\mathrm{are}\mathrm{convergent}\mathrm{sequences}\mathrm{with}{a}_k\to L\mathrm{and}{b}_k\to M\mathrm{as}k\to \infty$

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$\frac{a_k}{b_k}\to \frac{L}{M}$