Proof that the square of numbers ending with 5 ends with 25

Assume n is an integer and (10n + 5) is the number you want to square.

= 10n + 5

Pn is the nth pronic number as used in this proof.

Proof
$$\begin{align}(10n+5)^2&=(10n+5)(10n+5)\\&=100n^2+50n+50n+25\\&=100(n^2+n)+25\\&=100P_n+25\end{align}$$

Q.E.D

Example
n = 49 in this example

495&#178; = 100(49)(49+1)+25 = 245025