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 .