1. Set up an induction proof, prove the base case and set up the inductive step (say what the induction hypothesis would be, and what would need to be proved in the inductive step). Just set up the induction, you don't need to prove the inductive step. F (n - 1) * F (n + 1)- F(n)? = (-1)" 2. Set up an induction proof - prove the base case and set up the inductive step. Er (k . K!) = (n + 1)! -1 3. Prove a formula. Use induction to prove that the summation of (2i-1), with i going from 1 to n, is equal to n'. Note that this is the sum of the first n odd integers. Ek (2i - 1) = n *+ 2 4. Prove a formula. Use induction to prove that the summation of log(!), with i going from 1 to n, is equal to log(nl). ET, log (1) = log (n!) 5. Prove a formula. Use induction to prove that the summation of i " (n choose i), with i going from 0 to n, is equal to n * (2-). 6. Prove an inequality using strong induction. Use strong induction to prove that n = 0 7. Prove the area of the Koch snowflake. Define a sequence of polygons SO; $1 recursively, starting with SO equal to an equilateral triangle with unit sides. We construct Sn+1 by removing the middle third of each edge of Sn and replacing It with two-line segments of the same length Let an be the area of Sn. Observe that a0 is just the area of the unit equilateral triangle which by elementary geometry is p 3=4. So Prove by induction that for n >= 0, the area of the no snowflake is given by: a, = a. (8/5 - 3/5(4/9)"). 8. work out an inductive/recursive construction. Consider the problem of tiling a grid with triominoes. Suppose we want to tile the 8x8 grid with triominoes, leaving only the left/upper inner corner piece uncovered (the one on the fourth row from the top, fourth column from the left). Show the tiling produced by the inductive argument of Claim 40 in Building Blocks for this