Question

\(S=5+5^2+5^3+...+5^{2008}\)

S có chia hết cho 126 không? Vì sao?

Answer 1

\(S=5+5^2+5^3+..+5^{2008}\)

\(S=\left(5+5^2+5^3+5^4+5^5+5^6\right)+...\left(5^{2003}+5^{2004}+5^{2005}+5^{2006}+5^{2007}+5^{2008}\right)\)

\(S=5.\left(1+5+25+125+625+3125\right)+...+5^{2003}.\left(1+5+25+125+625+3125\right)\)

\(S=5.3906+...+5^{2003}.3906\)

\(S=3906.\left(5+...+5^{2003}\right)\)chia hết cho 126

=> S chia hết cho 3906 

Ủng hộ mk nha !!! ^_^

Answer 2

\(S=5+5^2+5^3+..+5^{2008}\)

\(S=\left(5+5^2+5^3+5^4+5^5+5^6\right)+...\left(5^{2003}+5^{2004}+5^{2005}+5^{2006}+5^{2007}+5^{2008}\right)\)

\(S=5.\left(1+5+25+125+625+3125\right)+...+5^{2003}.\left(1+5+25+125+625+3125\right)\)

\(S=5.3906+...+5^{2003}.3906\)

\(S=3906.\left(5+...+5^{2003}\right)\)chia hết cho 126

=> S chia hết cho 3906