IBM Ponder This #039 · July 2001

Find an exact expression for the infinite sum:

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

By "exact expression", I mean that "sqrt(2)" would be accepted
(if that were the right answer) but "1.414..." would not.

(This problem was posed by Saradakanta Ganguli, a long time ago.)

Solution

Best opened after a real attempt

To be added.