Give a closed expression for the infinite sum:

1/1 + 2/(2+3) + 3/(4+5+6) + 4/(7+8+9+10) + ...

Successive differences on the denominators shows them to follow a third degree polynomial.  That turns out to be (i^3+i)/2.  The terms are thus 2i/(i^3+i), which reduces to 2/(i^2+1).

Posted by Charlie on 2004-08-24 12:54:58