Bài 1:
a: \(10^9+10^8+10^7\)
\(=10^7\left(10^2+10+1\right)\)
\(=10^7\cdot111\)
\(=5^7\cdot2^6\cdot2\cdot111=5^7\cdot2^6\cdot222⋮222\)
b: \(S=5+5^2+5^3+...+5^{2012}\)
\(=\left(5+5^2+5^3+5^4\right)+\left(5^5+5^6+5^7+5^8\right)+...+\left(5^{2009}+5^{2010}+5^{2011}+5^{2012}\right)\)
\(=780+5^4\left(5+5^2+5^3+5^4\right)+...+5^{2008}\left(5+5^2+5^3+5^4\right)\)
\(=780\left(1+5^4+...+5^{2008}\right)\)
\(=65\cdot12\cdot\left(1+5^4+...+5^{2008}\right)⋮65\)
Bài 2:
a: \(S=5+5^2+5^3+...+5^{2006}\)
=>\(5\cdot S=5^2+5^3+5^4+...+5^{2007}\)
=>\(5\cdot S-S=5^2+5^3+...+5^{2007}-5-5^2-...-5^{2006}\)
=>\(4\cdot S=5^{2007}-5\)
=>\(S=\dfrac{5^{2007}-5}{4}\)
b:Đề sai rồi bạn
