Question

Cho S=5+5²+5³+5⁴+...+5²⁰⁰⁶

  a,Tính S

  b,CM S chia hết cho 126

Answer 1

\(S=5+5^2+5^3+5^4+...+5^{2006}\) 

\(5S=5^2+5^3+5^4+5^5+...+5^{2007}\)

\(5S-S=\left(5^2+5^3+5^4+5^5+...+5^{2007}\right)-\left(5+5^2+5^3+5^4+...+5^{2006}\right)\)

\(4S=5^{2017}-5\)

\(S=\frac{5^{2017}-5}{4}\)

Answer 2

\(S=5+5^2+5^3+5^4+....+5^{2006}\)

\(\Rightarrow5S=5\left(5+5^2+5^3+5^4+.....+5^{2006}\right)\)

\(\Rightarrow5S-S=\left(5^2+5^3+....+5^{2007}\right)-\left(5+5^2+5^3+....+5^{2006}\right)\)

\(\Rightarrow4S=5^{2007}-3\)

\(\Rightarrow S=\frac{5^{2007}-3}{4}\)