How can I deduce that this: (-1)^(n+1) +(-1)^(n-2) -(-1)^(n+3) is (-1)^n

Could I get a detailed answer please, with all the procedures?
Thanks!!!

The LOGICAL way to do this is to realize that (-1)^(n+1) and (-1)^(n-2) will always be opposites (+ and - 1), so they add up to 0. And -(-1)^(n+3) = (-1)^(n+4) = (-1)^n.

If you can't see this, you can do this:

(-1)^(n+1) +(-1)^(n-2) -(-1)^(n+3)
= (-1)^1 * (-1)^n + (-1)^(-2) * (-1)^n - (-1)^3 * (-1)^n
= -1 (-1)^n + 1 (-1)^n + 1(-1)^n
= (-1)^n

Case 1- Assume n to be an odd number
Do the math
n+1 and n+3 are even
n-2 and n are odd
Case 2- Assume n to be an even number
Do the math
n+1 and n+3 are odd
n-2 and n are even

Open your book and learn