Prove that the $\displaystyle (2n+1)$th term of the sequence $\displaystyle U_n=n^{2}-1$ is a multiple of $\displaystyle 4$.

How do I do this?

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- Oct 4th 2009, 10:33 AMViralSequential Proof
Prove that the $\displaystyle (2n+1)$th term of the sequence $\displaystyle U_n=n^{2}-1$ is a multiple of $\displaystyle 4$.

How do I do this? - Oct 4th 2009, 10:58 AMjames_bond
$\displaystyle U_{2n+1}=(2n+1)^2-1=4n^2+4n+1-1=4(n^2+n)$ So it is a multiple of 4.

- Oct 4th 2009, 10:59 AMViral
EDIT: Nevermind, I just realised what a fool I'm being. I'll try it again soon.

- Oct 4th 2009, 11:00 AMe^(i*pi)