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-1 ^ n

Is there any way of knowing what the value of (-1)^n is? As in is it positive or negative. I don't see why you could assume n is either odd or even. It's part of q5 of the step1 paper june 02

Reply 1

Bobifier

What exactly is the question?

Reply 2

noobynoo

(-1)^even = (-1)^(2n) = ((-1)^2)^n = 1^n = 1
(-1)^odd = (-1)^(2n+1) = (-1)((-1)^(2n)) = (-1)(1) = -1

Reply 3

und

Original post by jamie092

I don't see why you couldn't assume n is either odd or even.

Is that what you mean? If n/2 is an integer, n is even. If (n±1)/2 is an integer, n is odd.

When n is odd, (-1)^n is identical to -1.
When n is even, (-1)^n is identical to 1.

Sorry if I didn't quite answer your question, as I don't know what you mean exactly.