Chapter 6.2, Problem 1QR

To determine

To calculate:the sum ${\displaystyle \sum _{n=1}^5{n}^2}$ .

Answer to Problem 1QR

  $55$

Explanation of Solution

Given information:Given that ${\displaystyle \sum _{n=1}^5{n}^2}$

Formula used:Use formula ${\displaystyle \sum _{n=1}^n{n}^2}=\frac{n\left(2n+1\right)\left(n+1\right)}{6}$ .

Calculation: Hence,

  $\begin{array}{c}{\displaystyle \sum _{n=1}^5{n}^2}=\frac{5\left(2\cdot 5+1\right)\left(5+1\right)}{6}\\ =\frac{5\left(10+1\right)\left(5+1\right)}{6}\\ =\frac{5\cdot 11\cdot 6}{6}\\ =55\end{array}$

Therefore, ${\displaystyle \sum _{n=1}^5{n}^2}=55$