+0  
 
0
80
8
avatar+798 

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

 Jun 21, 2020
 #6
avatar+21951 
+1

The sum of n integers is:  n(n + 1)/2.

 

Placing that into the problem:  [ n(n + 1)/2 ] / [ 2n ]  =  10

 

Multiplying both sides by 2n:     n(n + 1)/2  =  20n

Multiplying both sides by 2:          n(n + 1)  =  40 n

Simplifying:                                     n2 + n  =  40 n

                                                    n2 - 39n  =  0

Factoring:                                    n(n - 39)  =  0

Possible answers:                     n = 0     n = 39

 

Obviously, 0 isn't correct, so:  n = 39

 Jun 21, 2020
 #7
avatar+798 
0

Thank you!

AnimalMaster  Jun 21, 2020

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