Practice Solution 8 -- Proofs by Induction

1. Prove 

Basis:Show the theorem holds for n=1.

 
Induction:
Assume the theorem holds for all n in the range 1 <= n <= k.

 
Show it works for n = k+1

 

 
 

2. Prove 

Basis:Show the theorem holds for n=1.

 
Induction:

Assume the theorem holds for all n in the range 1 <= n <= k


 
Show it works for n = k+1


 

 

3. Prove 

Basis: Show the theorem works for n=1

 
Induction:
Assume the theorem holds for 1 <= n <= k

 
Show the theorem holds for n = k + 1