Chapter 12.1, Problem 44E

To determine

Calculate the sum of the equation.

Answer to Problem 44E

The sum of the equation is $0$ .

Explanation of Solution

Given:

It is given in the equation that the equation is ${\displaystyle \sum _{j=1}^{100}{(-1)}^j}$ .

Concept Used:

In this use the concept of, putting the number in the equation and expand it.

Calculation:

Here, the equation is ${\displaystyle \sum _{j=1}^{100}{(-1)}^j}$ .

Put each and every number in the equation of k ,

  $\begin{array}{l}$ {\displaystyle \sum _{j=1}^{100}{(-1)}^j}={(-1)}^1+{(-1)}^2+{(-1)}^3+{(-1)}^4+\mathrm{...................}+{(-1)}^{99}+{(-1)}^{100}${\displaystyle \sum _{j=1}^{100}{(-1)}^j}=-1+1+(-1)+1+\mathrm{...................}+(-1)+1\\ {\displaystyle \sum _{j=1}^{100}{(-1)}^j}=-1+1-1+1+\mathrm{.......}-1+1\\ {\displaystyle \sum _{j=1}^{100}{(-1)}^j}=0\end{array}$

Conclusion:

The sum is $0$ .