Proof validation for number divisible by 25

I have to prove that is divisible by for .

My proof:

This expression is divisible by 25 for , so we look for .

is always number which last two digits will be .

So we can establish now for which value of n will last two digits be for number .

Since we have expression then last two digits of that expression will be:

If we now look at whole expression we will get:

For example lets take first expression too see if its divisible by 25, same proof is for other ones.

.....40 means that last two digits of that number is 40. .....40 - 15 have last two digits 25, so we have number which is divisible by 25. Same proof is for other numbers.

Is this proof valid?