Use mathematical induction to prove the following.=

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility:
S_n:  = 
S₁: 3 + 10 = 
S_k:  = 
S_k+1:  = 
1. Basis step: Since  =  = 13 = 3 + 10, S₁ is true.
2. Induction step: Let k be any natural number. Assume S_k. Deduce S_k+1.
= 
[3(k + 1) + 10] + = [3(k + 1) + 10] + 
= [3(k + 1) + 10] + 
 =  + 
 = 
 = 
 = 
 = 
 = .