CMSC 351 - Homework #1 - Due by 11:59pm on February 1st

Write clearly. Scan/photograph clearly. If we can't read it, we will grade it as incorrect.

After you finish your answers, scan or carefully photograph your answer sheets and create a single PDF with those images to upload to the ELMS entry.

If your Windows machine doesn't have a "Print to PDF" option, you might find the free CutePDF Writer useful.

You cannot e-mail them to me.

Even though you are uploading to the entry on ELMS, be sure to write your name and section clearly on the top of the first page.

We might not grade all questions.

(1) Use constructive induction to derive a formula for:

       n
       Σ i3
      i=1

    Show all of your steps and work.

    Note that any time we have a summation of something in the form 
    ix for some constant x that the sum can be calculated using a 
    polynomial where the largest term involves nx+1.

    HINT #1





                                  Phin - phin
(2)  Determine whether Fib(n) = ---------------
                                    sqrt(5)

                1+sqrt(5)              1-sqrt(5)
    given Phi = ---------   and  phi = ---------
                    2                      2

    using induction.  Clearly state the inductive hypothesis, what you
    will prove in the inductive step, and the show the details of that 
    proof.
 
    Remember, the 0th Fib number is 0 and the 1st is 1.

    HINT #2
    HINT #3