Nested Boxes

Just for those with a love of numbers, this one…I know you’re out there…

A toy is made from nested square boxes, as shown. The side of the outermost box is 10cm and the sides of the next one in touch the midpoints of the outer one.

Easy first. Find the sum of the perimeters of the first three boxes.
Harder. Find the sum of the perimeters of n boxes, n being a large number. It’s easy to see that this value will tend to one number, so your task is to find that number.

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3 thoughts on “Nested Boxes

  1. “It's easy…” ha. I was going to pass this on to HandyMan b/c this is right up his alley, but you already posted the answers. I didn't even get a chance to guess… which is ALL I would have done. lol

    Like

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