Question

Use strong induction to show that all dominoes fall in an infinite arrangement of dominoes if you know that the first three dominoes fall, and that when a domino falls, the domino three farther down in the arrangement also falls.

Short answer

The falling of dominos is true for infinite domino fall.

Step-by-step solution

Proof for basic step

The strong induction is based on the strong hypothesis of the mathematical induction. The strong induction is complete induction to proof

As three dominoes in arrangement falls due to fall of one domino so the propositional statement P(1), P(2) and P(3) are true.

Proof for Inductive step:

The given statement for falling is also true for k steps. Since the falling of domino is true for (k-1) step so it is also true for (k-2) step.

For every domino fall there is fall of three nest dominos in statement so

$P(k-2+3)=P(k+1)$

The above statement is true for (k+1) step so the strong induction is proved for fall of domino.

Therefore, the falling of dominos is true for infinite domino fall.