How do I prove that if $2\nmid n$ then $2|(n+1)$? I'd like to prove a very simple fact, but it's stumping me: namely, that if $2 \nmid n$ then $2\mid(n+1)$.
How would this usually be done?

If $n \not\equiv 0 \pmod2$, then $n+1 \not\equiv 1 \pmod2$, so we must have $n+1 \equiv 0 \pmod2$
