Dear r-soy,

In each of the problems you could simplify your last expressions further,

1)

Therefore the statement is true for P(k+1).

2)

Therefore the statement is true for P(k+1).

3) I think there is a bit of confusion in this problem. So I have done it from the beginning.

P(1) : Left hand side =

Right hand side =

Therefore the statement is true for P(1).

Suppose that the statement is true for P(k). Then,

Therefore,

Therefore the statement is true for P(1).

Hope this will help you.