Let's consider an example to understand how dynamic programming works. We use the Fibonacci series to illustrate both the memoization and tabulation techniques.

The Fibonacci series can be demonstrated using a recurrence relation. Recurrence relations are recursive functions that are used to define mathematical functions or sequences. For example, the following recurrence relation defines the Fibonacci sequence [1, 1, 2, 3, 5, 8 ...]: 

func(1) = 1
func(0) = 1 
func(n) = func(n-1) + func(n-2)

Note that the Fibonacci sequence can be generated by putting the values of n in sequence [1, 2, 3, 4, ...].