# For which n does 1+2+...+n divide 1*2+2*3+...(n-1)n

• Nov 29th 2007, 05:07 AM
james_bond
For which n does 1+2+...+n divide 1*2+2*3+...(n-1)n
For which $n$ does $\sum_{i=1}^ni$ divide $\sum_{i=1}^n(i-1)i$ ?
• Nov 29th 2007, 05:17 AM
galactus
Take note that

$\frac{\sum_{i=1}^{n}i}{\sum_{i=1}^{n}(i-1)i}=\frac{\frac{n(n+1)}{2}}{\frac{n(n-1)(n+1)}{3}}=\frac{3}{2(n-1)}$