Chapter 8, Problem 5CR

To determine

Find the sum of the given series.

Answer to Problem 5CR

The sum of the given series is $1081$ .

Explanation of Solution

Given:

The given series is ${\displaystyle \sum _{i=1}^{46}i}$ .

Calculation:

  ${\displaystyle \sum _{i=1}^{46}i}$

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

In the given series $n=46$ .

  $\begin{array}{l}{\displaystyle \sum _{i=1}^{46}i}=\frac{46\left(46+1\right)}{2}\\ =\frac{46\cdot 47}{2}\\ =23\cdot 47\\ =1081\end{array}$

Hence the sum of the given series is $1081$ .