Here is another typical sum puzzle from Presh Talwalkar.

“Solve the following sums:

_____1/(1×3) + 1/(3×5) + 1/(5×7) + 1/(7×9) + 1/(9×11) =

_____1/(4×7) + 1/(7×10) + 1/(10×13) + 1/(13×16) =

_____1/(2×7) + 1/(7×12) + 1/(12×17) + … =”

The only reason I am including this puzzle is that Talwalkar gets very excited about deriving a formula that can solve sums of this type.  This gives me an opportunity to discuss the “formula vs. procedure” way of doing math.

See the Incredible Trick Puzzle