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

$\left(a_k+b_k\right)\to$

Short answer

The required answer is$\left(a_k+b_k\right)\to L+M$

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,$\left(a_k+b_k\right)\to L+M$