There's a question I've been having difficulty solving, and I would really appreciate if you can show he steps to how I can achieve the answer.
QUESTION: The numbers 1, 4, 10, 20, and 35 are called tetrahedral numbers because they are related to a four sided shape called a tetrahedron. Determine a mathematic model that you can use to generate the nth tetrahedral number.
The triangular numbers are
1,3,6,10,...
So, the nth tetrahedral number is the sum of the first n triangular numbers.
The nth triangular number is the sum of the first n integers (1+2+3+...) = n(n+1)/2
It is clear that the nth tetrahedral number will be a cubic expression in n.
The nth integer is n/1!
The nth triangular number is n(n+1)/2!
The nth tetrahedral number is n(n+1)(n+2)/3!
and so on.
This can easily be proven using induction.