Question

2[(-1)^n+1]

how to simplify?

Answer 1

if n is even, then (-1)^(n+1) = -1

if n is odd, then (-1)^(n+1) = +1

if n is not an integer, then (-1)^(n+1) is undefined

So,
if n is even, your expression is -2
if n is odd, your expression is +2