If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?

Generally Geometric

Age 16 to 18 Challenge Level:

Differentiating the known sum, then differentiating the series term
by term and multiplying by $x$ gives the first result. I f this
method works once it will work twice or $k$ times.