Sum of Infinite Series

["Paul O. Johnson" <pojhome@SWBELL.NET>]

This is a math question. Please bear with me. I can't find the answer in any of my few physics and math reference books. Since it's based on center of gravity and stability principles, I feel emboldened to ask it here.

 

I am creating a tabletop exhibit at The Science Place. It consists of eight identical rectangular wooden blocks (about 8 inches long). The object is to create an "impossible stairway" by stacking the blocks so that the top block extends beyond the supporting edge of the bottom block. It looks unstable but it ain't.

 

The theoretical best solution is to stack the blocks from the top down so that the steps get shorter as you work your way down. The top step (between blocks 1 and 2) is 1/2 block-length, the next step down (between blocks 2 and 3) is 1/4 block-length, then 1/6, 1/8, 1/10, 1/12, and finally 1/14 block-length between blocks 7 and 8.

 

I want to state in the exhibit's sign what the absolute maximum extension is. This requires that I sum the infinite series 1/2 + 1/4 + 1/6 + 1/8 + . . . I'm ashamed to admit that I no longer carry this trivial math equation in my head (I know I once did). Can anyone help me?

 

Paul O. Johnson

Exhibit Developer

The Science Place

Dallas, Texas