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 20040824 12:54:58 