1. In class I computed the binomial coefficients when s = 1.2. Recompute those on your own without looking at the formulas for the binomial coefficients.

2. Suppose s = 0.2. Compute the 1st through 5th binomial coefficients.
   Use the telescopic property of the binomial coefficient to compute these.

   ANSWERS:

   You will need those results in one of the examples.

3. We saw that   Δf₀   =   f₁ – f₀.
   1. Show that   Δ²f₀   =   f₀ – 2 f₁ + f₂ .    We will need that result in a later topic.
      Does this formula look a little familiar? Where have we seen a formula like this before?    (Hint: revisit Aitken acceleration.)
      Follow-up question:    Based on this result, what is   Δ²f₄ ?

   2. Show that   Δ³f₀   =   – f₀ + 3f₁ – 3f₂ + f₃ .    We will need that result in a later topic.
      Follow-up question:    Based on this result, what is   Δ³f₆ ?
   
   In Problem 3 we say we are "eliminating the differences" (expressing them in terms of just f values).
   

   We will use all the above in a later chapter.