According to the given information it is required to prove the following using principle of mathematical induction.
If is a positive ineger then divisible by 17.
that is: is divisible by 17
For n = 1
17 is diviseble by 17
so, the statement is true for n=1
Let us assume that the given statement is true for n = k that is:
is posisitve integer then is divisible by 17
Now, prove that the statement is true for n = k+1:
is divisible by 17 and from assumption is divisible by 17
hence, is diviseble by 17
Therefore, whenever n = k is true n = k+1 is true.
Therefore, it is true for all integers.