For 1.

P(k)

P(k+1)

Show that "if" P(k) is valid, then P(k+1) "must therefore" also be valid.

Hence, write P(k+1) in terms of P(k).

Proof

If P(k) is valid, then

If , then P(k+1) will be valid.

If

then

It can be seen that this is true since

hence, you need to examine the case for