The young Gauss was so smart and mathematically intuitive, he must have been a nightmare to have in class…take a look here.
The explanation you are looking for is here.
Can this get any more fun…?
Here is some stuff about the binomial theorem.
Patrick Andrews has a PhD in Mechanical Engineering from Heriot-Watt University and an MSc in Neuroscience from the University of Cambridge.
A former Chartered Engineer and Chartered Mathematician, Patrick has worked in management consultancies and high-tech startups, and in academia as a postdoc in Applied Mathematics at Cambridge and a maths lecturer at De Montfort University.
Patrick is the father of three delightful (but not uniformly mathematical!) daughters.