Use mathematical induction to prove that the statement is true for every positive integer n.1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8n = 

What will be an ideal response?

S1:1 ? 8 
 8 
 8 = 8 ?
Sk: 1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8k = 
Sk+1: 1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8(k + 1) = 
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
8(k+1), to both sides."

1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8k + 8(k + 1) =  + 8(k + 1)
1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8(k + 1) =  + 
1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8(k + 1) = 
1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8(k + 1) = 
We have shown that if we assume that Sk is true, and we add (8(k+1) to both sides of Sk , then Sk+1 is also true. By the principle of mathematical induction, the statement Sn is true for every positive integer n.

Mathematics

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