Improve algorithm explanation

This is a follow-up issue from !60 (merged). We should improve how we introduce the algorithm. Specifically we should take a look at the following.

• The motivation and the intuition behind the algorithm may be not clear.
• The notation may be hard to follow.
• We may benefit from concrete illustrations: writing explicit expressions for higher order terms and counting the number of matrix products we use.
• We should probably be more explicit that we're talking about a cost per extra order, assuming that all lower orders are already computed.