+865 For what positive integer n is \(\frac{1+2+3+\ldots + n}{2n} = 10\) true?
+23252 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
