Hi there.

Soon I have my final exam in Discrete Mathematics, and I'm just working a little bit on proof by induction and refreshing my algebra. There are two exercises that I have some troubles with, and hope that you guys/girls could help me. By the way, sorry if my english is a bit rusty (norwegian).

Exercise 1:

For each natural number n, let.Prove thatfor all .

Incomplete answer (Exercise 1):

I'm going to prove that.Proof:What now? How can I make ? Maybe I have done something wrong in the process, or is it my algebra skills?

Exercise 2:

Prove by induction thatfor all . Hint: Use that .

Very incomplete answer (Exercise 2):

Base step:.The claim is true for n = 1.

Inductive step:

...

Hehe, I'm stuck right here... Hope someone can help me =D

Thanks!