Chapter F, Problem 26E

Find the value of the sum.

26. ${\displaystyle \underset{i=1}{\overset{100}{\sum }}4}$

To determine

To find: The value of the sum ${\displaystyle \sum _{i=1}^{100}4}$.

Answer to Problem 26E

The value of the sum ${\displaystyle \sum _{i=1}^{100}4}$ is $400$.

Explanation of Solution

Definition used:

If $a_m,a_{m+1},\mathrm{...},a_n$ are real numbers and m and n are integers such that $m\le n$, then ${\displaystyle \sum _{i=m}^n{a}_i=a_m+}{a}_{m+1}+a_{m+2}+\cdots +a_{n-1}+a_n$.

Calculation:

By the above definition, the sum ${\displaystyle \sum _{i=1}^{100}4}$ expressed as follows.

$\begin{array}{c}{\displaystyle \sum _{i=1}^{100}4}=\underset{\left(100\text{times}\right)}{\underbrace{4+4+4+\cdots +4}}\\ =100\cdot 4\\ =400\end{array}$

Thus value of the sum ${\displaystyle \sum _{i=1}^{100}4}$ is $400$.