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

AnimalMaster Jun 21, 2020

#6**+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: n^{2} + n = 40 n

n^{2} - 39n = 0

Factoring: n(n - 39) = 0

Possible answers: n = 0 n = 39

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

geno3141 Jun 21, 2020