Writing the Terms of a Sequence

Write the first six terms of the sequence: \( \{ b_{n}\} = \left\{ ( -1) ^{n-1} \, \dfrac{2}{n} \right\} \)

Solution \( \begin{array}[t]{lllll} b_{1}= ( -1) ^{0}\,\dfrac{2}{1}=2 & &\qquad b_{2}= ( -1) ^{1}\, \dfrac{2}{2}=-1 & &\qquad b_{3}= ( -1) ^{2}\,\dfrac{2}{3}=\dfrac{2}{3} \\[7pt] b_{4}=-\dfrac{1}{2} & &\qquad b_{5}=\dfrac{2}{5} & &\qquad b_{6}=-\dfrac{1}{3} \end{array} \)

The first six terms of the sequence are \(2,-1,\,\dfrac{2}{3},-\dfrac{1}{2},\, \dfrac{2}{5},-\dfrac{1}{3}\).