Please help with a proof

Mos5180d

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Mar 14, 2019
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Seems pretty basic, maybe I’m missing something.

I need to prove that (-1)^(x+1) = -(-1)^x

I can do it separately
If x is even then -1=-1
If x is odd then 1=1

But can it be done in one go?
Thanks
 

Dr.Peterson

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Nov 12, 2017
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Apply the exponent rule a^(m+n) = a^m * a^n.
 

Mos5180d

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Mar 14, 2019
Messages
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Apply the exponent rule a^(m+n) = a^m * a^n.
Something simple as I thought! Thank you very much, this has finished off a proof I’ve been doing for quite a while
 

Jomo

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Dec 30, 2014
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If x is even then -1=-1
If x is odd then 1=1
-1 = -1 always. It does NOT depend on the parity of x.
1 = 1 always. It does NOT depend on the parity of x.
 

Dr.Peterson

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Nov 12, 2017
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I need to prove that (-1)^(x+1) = -(-1)^x

I can do it separately
If x is even then -1=-1
If x is odd then 1=1
For clarity, I think what you meant was this proof by cases:

If x is even then (-1)^(x+1) = -(-1)^x becomes -1=-1, which is true;​
If x is odd then (-1)^(x+1) = -(-1)^x becomes 1=1, which is true;​
so the statement is true in all cases.​

That is a valid method of proof, though clearly not as efficient in this case as you wished.
 
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