03/06/2011, 03:24 PM
3. 2 [n] 2 = 4
Proof:
2 [1] 2 = 2 + 2 = 4
Suppose 2 [n] 2 = 4 for a given n, then we wish to prove that 2 [n+1] 2 is also 4.
2 [n+1] 2 = 2 [n] (2 [n+1] 1) = 2 [n] 2 = 4
So it is proven by induction.
Proof:
2 [1] 2 = 2 + 2 = 4
Suppose 2 [n] 2 = 4 for a given n, then we wish to prove that 2 [n+1] 2 is also 4.
2 [n+1] 2 = 2 [n] (2 [n+1] 1) = 2 [n] 2 = 4
So it is proven by induction.

