Question

b) Chứng tỏ : \(N=5^1+5^2+5^3+5^4+...+5^{2010}⋮31\)

Answer 1

Ta có :

\(N=5+5^2+5^3+....+5^{2010}\)

\(\Rightarrow N=5\left(1+5+5^2\right)+.....+5^{2008}\left(1+5+5^2\right)\)

\(\Rightarrow N=5.31+....+2^{2008}.31\)

=> N chia hết cho 31

Answer 2

\(N=5^1+5^2+5^3+5^4+...+5^{2010}\)

\(=5\left(1+5+5^2\right)+5^4\left(1+5+5^2\right)+...+5^{2018}\left(1+5+5^2\right)\)

\(=31\left(5+5^4+...+5^{2018}\right)⋮31\)

=>đpcm