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(-1)^n+1 x n = 50

Guest May 25, 2015

Best Answer 

 #1
avatar+26741 
+10

n = 51

 

$${\left(-{\mathtt{1}}\right)}^{{\mathtt{51}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{51}} = {\mathtt{50}}$$

.

Alan  May 26, 2015
 #1
avatar+26741 
+10
Best Answer

n = 51

 

$${\left(-{\mathtt{1}}\right)}^{{\mathtt{51}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{51}} = {\mathtt{50}}$$

.

Alan  May 26, 2015
 #2
avatar+92748 
0

That is neat Alan  

Melody  May 26, 2015
 #3
avatar+87293 
+5

Notice that this wouldn't be too difficult to solve........the first term is either -1 or 1.....

 

Let's suppose it was 1.....then "n" would have to be even........rearranging the equation, we have

 

n = 50 - 1   = 49.......but this is a contradiction, because n is even

 

If n were odd, we would have {again, rearranging}

 

n = 50 + 1........and this must be the solution, because  

 

(-1)^51 + 51 = 50     →  -1 + 51  = 50     ..... which is true.....!!!

 

 

CPhill  May 26, 2015

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