Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7n = 
What will be an ideal response?
| S1: | 1 ? 7   |
7 = 7 ?
Sk: 1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7k =
Sk+1: 1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7(k + 1) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
7(k+1), to both sides."
1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7k + 7(k + 1) =
+ 7(k + 1)1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7(k + 1) =
+ 
1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7(k + 1) =
1 ? 7 + 2 ? 7 + 3 ? 7 + . . . + 7(k + 1) =
We have shown that if we assume that Sk is true, and we add (7(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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A. 
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C. 
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