What is solution of (-1)^n (n is for all integer)...?

____________________________________

Explanation

Let us see the solution of -1 base to power 2 and 3.

We know that 
        2
    (-1)  = 1
And 
        3
    (-1)  = -1

therefore -1 to any EVEN power answer will 1 and -1 to any ODD power answer will -1. By putting this rule to all integers. We get ...

                                   _
        n                           |
    (-1) = 1      if n is EVEN      |
       n                             >
    (-1) = -1     if n is ODD       |  
                                   _|

Final answer will be 1 when n is EVEN and -1 when n is ODD.

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      -------------- = ?
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             _____________________
            /      _____________  
           /     /        ____
          /     /        /  2  
         /  4  /  4  .  / 4  
        /    \/       \/
       /  --------------------
      /            3
    \/            2    

    

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Worksheets (Solved)

Matrix Logarithm

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