9. The last 2 digits of
$$
2005+2005^{2}+2005^{3}+\cdots+2005^{2005}
$$
is:
(a) 00 ;
(b) 05 ;
(c) 25 ;
(d) 50 ;
(e) 75 .
9 Ans: (b).
The last 2 digits of $2005^{n}$ is 25 except $n=1$ which gives 5 . Hence the last 2 digits is $5+2004 \times 25(\bmod 100)=05$.