Chapter 9.1, Problem 2QR

To determine

To find: The first four terms and the 30^th term of the sequence.

Answer to Problem 2QR

The first four terms and the 30^th term of the sequence ar $u_1=-1,u_2=\frac{1}{2},u_3=-\frac{1}{3},u_4=\frac{1}{4}\text{and}{u}_{30}=\frac{1}{30}$respectively.

Explanation of Solution

Given information: $u_n=\frac{{\left(-1\right)}^n}{n}$

Concept used: Any term of the sequence can be determined by substituting that term in the sequence.

Calculation:

Substitute $n=1$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_1=\frac{{\left(-1\right)}^1}{1}\\ =-1\end{array}$

Substitute $n=2$ into the given sequence and simplify it to determine the second term of the sequence.

  $\begin{array}{c}{u}_2=\frac{{\left(-1\right)}^2}{2}\\ =\frac{1}{2}\end{array}$

Substitute $n=3$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_3=\frac{{\left(-1\right)}^3}{3}\\ =-\frac{1}{3}\end{array}$

Substitute $n=4$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_4=\frac{{\left(-1\right)}^4}{4}\\ =\frac{1}{4}\end{array}$

Substitute $n=30$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_{30}=\frac{{\left(-1\right)}^{30}}{30}\\ =\frac{1}{30}\end{array}$