Use mathematical induction to prove that the statement is true for every positive integer n.4 + 
+ 
+ . . . + 
= 5
What will be an ideal response?
| S1: | 4  5 |
5
4 = 4 ?
Sk: 4 +
+ 
+ . . . + 
= 5
Sk+1: 4 +
+ 
+ . . . + 
= 5
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
to both sides.4 +
+ 
+ . . . + 
+ 
= 5
+ 
4 +
+ 
+ . . . + 
= 5 - 
+ 
4 +
+ 
+ . . . + 
= 
4 +
+ 
+ . . . + 
= 
4 +
+ 
+ . . . + 
= 
- 
4 +
+ 
+ . . . + 
= 5 - 
4 +
+ 
+ . . . + 
= 5
We have shown that if we assume that Sk is true, and we add
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.
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