Question

Asked Jun 2, 2019

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**A) determine which amounts of postage can be formed using just 3 - cent and 10 - cent stamps.**

3,6,9,10,12,13,15,16,18,19,21,23,24,26,27,29,30,...,L*3+H*10

**B) prove your answer to (A) using the principal of mathematical induction. Be sure to state explicitly your inductive hypothesis and the inductive steps.**

Step 1

B)

__Known fact:__

*Base step*: Show it is true for first case, usually *n* =1.

*Induction step*: Show that if *n* = k is true then *n* = *k*+1 is also true.

Step 2

__Base step:__

Let us show the induction is true for *P*(19).

*P*(19) = one 10 cent stamp + three 3 cent stamps.

__Induction step:__

Let us assume that the induction is true for *n*.

That is, *n* postage amount can be formed using 10 cents and 3 cents stamps.

Now it is necessary to show that the induction is true for *n* + 1.

Step 3

*Case 1:*

If there are no 10 cents in *n*, then remove three cents stamps and add one 10 cent stamps to get *n +*1.

If n=18,

P(18) = six 3 cents stamp

There is no 10 cents stamps thus, remove three 3 cents stamp and add one 10 cents.

That is, P(18) = six 3 cents stamp – three 3 cent stamp + one 10 cents stamp.

&nbs...

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