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For what positive integer \(n\) is \(\frac{1+2+3+\ldots + n}{2n} = 10\) true?

 

Thanks 

-PharaoCarl

 May 13, 2020
 #1
avatar+111438 
+2

The numerator  can be written as the sum

 

(n) (n + 1)  / 2        so we have

 

(n)(n + 1)

________  =   10      simplify

2 * 2n

 

n + 1

_____      =    10       multiply both sides by  4

  4

 

n + 1  =  40

 

n = 39

 

 

cool cool cool

 May 13, 2020

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