Use mathematical induction to prove the following.
= 
What will be an ideal response?
Answers may vary. One possibility:
Sn: 
= 
S1: 7 + 5 = 
Sk: 
= 
Sk+1: 
= 
1. Basis step: Since 
= 
= 12 = 7 + 5, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
= 
[7(k + 1) + 5] + 
= [7(k + 1) + 5] + 
= [7(k + 1) + 5] + 
= 
+ 
= 
= 
= 
= 
= 
.
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