avem 2001 termeni , ii putem grupa cate 3 (2001:3=667)
N=1+5+ 5^2+ 5^3 + 5^4 +...+ 5^2000=
=(1+5+ 5^2)+ 5^3(1 + 5 +5^2)+...+5^1998(1+5+ 5^2)=
=(1+5+ 25)+ 5^3(1 + 5 +25)+...+5^1998(1+5+ 25)=
=31+ 5^3×31+...+5^1998×31=
=31×(1+ 5^3+...+5^1998) deci divizibil cu 31