What are the last two digits of (1+5^(2n+1))/6?
Note that n is assumed to be any positive integer.

Factor the numerator as (1+5)(1-5+...+5^2n) and note that positive powers ending in 25 are offset by negatives.  You're left with (1-5+25)=21 since the (1+5) factor cancels.  

Posted by xdog on 2013-09-04 12:22:43