# Show that there is no value of n for which

Question:

Show that there is no value of $n$ for which $\left(2^{n} \times 5^{n}\right)$ ends in 5 .

Solution:

We can write:

$\left(2^{n} \times 5^{n}\right)=(2 \times 5)^{n}$

$=10^{n}$

For any value of n, we get 0 in the end.

Thus, there is no value of $n$ for which $\left(2^{n} \times 5^{n}\right)$ ends in 5 .