Answer
$\frac{1}{25}$
Work Step by Step
I plug in the respective values of $x$ into $f(x)=(-1)^{x+1}(\frac{1}{x^2})$
For $x=1$: $f(x)=(-1)^{1+1}(\frac{1}{1^2})=1\cdot\frac{1}{1}=1$
For $x=2$: $f(x)=(-1)^{2+1}(\frac{1}{2^2})=-1\cdot\frac{1}{4}=-\frac{1}{4}$
For $x=3$: $f(x)=(-1)^{3+1}(\frac{1}{3^2})=1\cdot\frac{1}{9}=\frac{1}{9}$
For $x=4$: $f(x)=(-1)^{4+1}(\frac{1}{4^2})=-1\cdot\frac{1}{16}=-\frac{1}{16}$
For $x=5$: $f(x)=(-1)^{5+1}(\frac{1}{5^2})=1\cdot\frac{1}{25}=\frac{1}{25}$
