Chapter 12, Problem 25RE

To determine

To find: The sum of the given expression.

Answer to Problem 25RE

The sum of the expression is $3825$ .

Explanation of Solution

Given:

The given expression is,

  ${\displaystyle \sum _{k=1}^{50}3k}$

Calculation:

Consider the given expression is,

  ${\displaystyle \sum _{k=1}^{50}3k}$

Rewrite the above expression as,

  $3{\displaystyle \sum _{k=1}^{50}k}$

The general from for the expression ${\displaystyle \sum _{k=1}^{n}k}$ is,

  ${\displaystyle \sum _{k=1}^{n}k}=\frac{n\left(n+1\right)}{2}$

Then,

  $\begin{array}{c}3{\displaystyle \sum _{k=1}^{50}k}=3\left[\frac{50\left(50+1\right)}{2}\right]\\ =3\left(1275\right)\\ =3825\end{array}$

Thus, the sum is $3825$ .