$\displaystyle x_n=(-1)^n$ and $\displaystyle f(x)=x^3$

does the sequence $\displaystyle f(x_n)$ converge(to anything)? I know $\displaystyle x_n$ doesn't converge to anything. is $\displaystyle f(x_n)=x_nx_nx_n$?

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- Dec 10th 2009, 11:07 AMcharikaarconverge
$\displaystyle x_n=(-1)^n$ and $\displaystyle f(x)=x^3$

does the sequence $\displaystyle f(x_n)$ converge(to anything)? I know $\displaystyle x_n$ doesn't converge to anything. is $\displaystyle f(x_n)=x_nx_nx_n$? - Dec 10th 2009, 11:09 AMMoo
Hello,

$\displaystyle f(x_n)=(x_n)^3=[(-1)^n]^3=[(-1)^3]^n=(-1)^n$