Use mathematical induction to prove that the statement is true for every positive integer n.4 +  +  + . . . +  = 5

What will be an ideal response?


S1:5
 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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