Name: Espera Pax
Question: Deduction is drawing a conclusion from something known or assumed. This is the type of reasoning we use in almost every step in a mathematical argument. For example to solve 2x = 6 for x we divide both sides by 2 to get 2x/2 = 6/2 or x = 3. What we know or assume is that 2x = 6 and that you can divide both sides of an equation by any nonzero number and the equation is still valid. From these two facts we deduce that x = 3. Mathematical induction is a particular type of mathematical argument. It is most often used to prove general statements about the positive integers. For example you could use mathematical induction to prove that for every positive integer n, or that for every positive integer n, To illustrate a proof by induction I want to prove the second statement above. The first thing I would do, before starting a proof, is to experiment to see if the statement is reasonable.
Proof by mathematical induction proceeds in two steps. Step 1
7 divides 7*11^{k} and, by assumption, 7 divides 11^{k}  4^{k}, thus 7 divides 11^{k+1}  4^{k+1} It follows that for any positive integer n, 7 divides 11^{n}  4^{n} I hope this helps,Harley
