Inductive proofs not involving summation or product series

  1. Study this example and be able to eventually DO the proof perfectly without looking at your notes. Key word (EVENTUALLY). Try it again and again without notes UNTIL you get it perfectly correct and you will be comfortable with the pattern of inductive proofs! Your algebra will no longer be quite so rusty either! :-)

  2. Your 2 cents worth, or 3 cents worth and postage made up of only 2 and 3 cent stamps. Inductive proofs and the IH Inductive Hypothesis in yet another context.

  3. Inductive Proof Postage Problem from page 111 of textbook. Exercise #64. (FRIDAY, FEBRUARY 27th CLASS). STUDY and REWRITE and REVIEW THIS proof frequently and VERY CAREFULLY!)

  4. Another example proof for Induction problems. Prove that the predecessor of (7 raised to the nth power) is always divisible by 6, for all integers n >= 1. (FRIDAY, FEBRUARY 27th HANDOUT - MASTER THIS PROOF on a higher level every time you review it). Rewrite this proof. Appreciate every detail of the proof. REVIEW!!!

  5. Inductive proof of an inequality from November 14th class group exercise.
    (COVERED ON FRIDAY, FEB 27th - REVIEW, REVIEW, REVIEW this proof).

  6. Postage stamp problems and coming up with the TWO DIFFERENT CASES for the Inductive Step of the proof. Includes a Visual Basic program for calculating the needed cases for the Inductive Step of the proof. You DO NOT have to understand the program, but it does show that Inductive proofs about Postage Stamps are NOT MAGIC!

  7. Postage 7 cents and 11 cents Visual Basic program, with sample output. Yet another attempt to show that postage inductive proofs are NOT MAGIC. Shows 1 cent differences for 11 and 13 and shows it for 19 and 23 cents stamps too. :-)

  8. Divisible by 3 inductive proof from the Wednesday, 11/14/2001 class.

  9. Inductive HW hints and email note. Helpful for summation notation issue and for algebra of factorial and exponential issues.

  10. Summation notation inductive proof that 1 + 3 + ... + 2n-1 = n*n. Understanding summation notation.

  11. Summation and inductive proof that 1 + 2 + ... + n = (n(n+1))/2 is an example to be studied.

  12. Here is the 2nd Principle of Mathematical Induction Proof illustrated. You do NOT need to understand this approach, but it is discussed in the book.