Question

Show that 9^n can't end with 2 for any integer n.

Answer 1

hope this answers your question

Answer 2

Answer:

Proof shown below.

Step-by-step explanation:

To show : That $9^n$ can't end with 2 for any integer n.

Proof:

Let, p(n) denotes the statement that $9^n$ cannot end with 2 for any positive integer n.

For n=1,

p(1): 9¹=9, not ended with 2.

Let us assume that p(n) is true for n=k

i.e., $9^k$ can not ended with 2.

For n=k+1,

p(k+1):  $9^{k+1}=9^k.9$

which can not be ended with 2.

since  $9^k$ is not ended with 2.

Now p(1) is true and p(k+1) is true if p(k) is true.

Then by the principle of mathematical induction $9^n$ can not be ended with 2 for any positive integer n.

For example :

$9^1=9\\9^2=81\\9^3=729\\....$