Question

In Problems 71–82, find the sum of each sequence.

$\sum _{k=1}^{40}5$

Short answer

The sum of this sequence is 200.

Step-by-step solution

Step 1. Write the given information.

The sum of sequence:$\sum _{k=1}^{40}5;k=1,...,40$

Step 2. Use the formula for sum of sequence. 

The formula for summation is:

$$\begin{gathered} \underset{k=1}{\overset{n}{\sum c}}=c+c+...+c \\ \Rightarrow \underset{k=1}{\overset{n}{\sum c}}=cn,c-realnumber \end{gathered}$$

Step 3. Use the formula with c=5 and n=40.

Using the formula gives:

$$\begin{gathered} \underset{k=1}{\overset{40}{\sum 5}}=5+5+...+5 \\ \Rightarrow \underset{k=1}{\overset{40}{\sum 5}}=5\times 40 \\ \Rightarrow \underset{k=1}{\overset{40}{\sum 5}}=200 \end{gathered}$$