Use mathematical induction to prove the statement is true for all positive integers n.7 + 14 + 21 + . . . + 7n = 
What will be an ideal response?
Answers may vary. Possible answer:
First, we show the statement is true when n = 1.
For n = 1, we get 7 = 
Since 
= 
= 7, P1 is true and the first condition for the principle of induction is satisfied.
Next, we assume the statement holds for some unspecified natural number k. That is,
Pk: 
is assumed true.
On the basis of the assumption that Pk is true, we need to show that Pk+1 is true.
Pk+1: 
So we assume that 
is true and add the next term, 
to both sides of the equation.
7 + 14 + 21 + ... + 7k + 7(k + 1) = 
+ 7(k + 1)
7 + 14 + 21 + ... + 7k + 7(k + 1) = 7
7 + 14 + 21 + ... + 7k + 7(k + 1) = 
The last equation says that Pk+1 is true if Pk is assumed to be true. Therefore, by the principle of mathematical induction, the statement 7 + 14 + 21 + ... + 7n = 
is true for all natural numbers n.
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