More on Recursive Functions:

     In this week we learned not only how to proof recursive functions but also how to define them. it is getting very complicated indeed, since it needs plenty of thinking it through and trying it out on many different values to make sure that you came up with the right formula for the recursive function. I find it a little easier to actually read the questions out loud and start drawing pictures or numbers on paper of the expected results. so if you have a better and easier way to do this, please let me know.

     After I do the above step and solve the problem I begin trying it with different type of values for (n) from smallest to some of the higher values. this was an example to help me under stand the whole divide and conquer recurrences from Introduction to the Theory of Computation book
the functions started looking like this:

   then it became in a closed form and looked like this:

then with mathematical substitutions we came out with the final T(n) that looks like this:

I hope for next week we won't take new topics and work more on these problems and on how to solve them.