Ken's blog

An eccentric billionaire decided to build two tall pointed towers consisting of a series of stacked cubes. They would serve decorative purposes being placed in parallel at a large futuristic gate in his theme park. The material to be used would be a high-strength, transparent nanomaterial. The billionaire stated that rainwater and some kind of energy would be collected for undisclosed purposes.

The first cube was to have a side length of 1 cm, the subsequent cube sides 1 cm greater than the previous, up to the last cube with a side length of 100 cm.

The architect scratched his head thinking how to add up the volumes. Can you help him greatly simplify the calculations?

What would be the height of the towers, and their combined volume?