Question

s=5+5^2+5^3+...+5^2004

chứng minh rằng : s chia hết 126

 

Answer 1

Ta có: \(S=5+5^2+5^3+...+5^{2004}\)

\(=\left(5+5^2+5^3+5^4+5^5+5^6\right)+\left(5^7+5^8+5^9+5^{10}+5^{11}+5^{12}\right)...+\left(5^{1999}+5^{2000}+5^{2001}+5^{2002}+5^{2003}+5^{2004}\right)\)

\(=5\left(1+5+...+5^5\right)+5^7\left(1+5+...+5^5\right)+...+5^{1999}\left(1+5+...+5^5\right)\)

\(=\left(1+5+...+5^5\right)\left(5+5^7+...+5^{1999}\right)\)

\(=3906\cdot\left(5+5^7+...+5^{1999}\right)\)

mà \(3906⋮126\)

nên \(S⋮126\)

Answer 2

alo