Write out the first five terms of the sequence.
-$$\left\{ ( - 1 ) ^ { n - 1 } \left( \frac { n + 1 } { 2 n - 1 } \right) \right\}$$
A) $- 2,1 , \frac { 4 } { 5 } , - \frac { 5 } { 7 } , \frac { 2 } { 3 }$
B) $2 , - 1 , \frac { 4 } { 5 } , - \frac { 5 } { 7 } , \frac { 2 } { 3 }$
C) $2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$
D) $- 2,1 , - \frac { 4 } { 5 } , \frac { 5 } { 7 } , - \frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

The sequence is given by $(-1)^{n-1} \left(\frac{n+1}{2n-1}\right)$. For $n=1$, the term is $2$; for $n=2$, the term is $-1$; for $n=3$, the term is $\frac{4}{5}$; for $n=4$, the term is $-\frac{5}{7}$; and for $n=5$, the term is $\frac{2}{3}$.

Write Out the First Five Terms of the Sequence {(−1)n−1(n+12n−1)}\left\{ ( - 1 ) ^ { n - 1 } \left( \frac { n + 1 } { 2 n - 1 } \right) \right\}{(−1)n−1(2n−1n+1​)}

Write Out the First Five Terms of the Sequence $\left\{ ( - 1 ) ^ { n - 1 } \left( \frac { n + 1 } { 2 n - 1 } \right) \right\}$