Question

Tổng 3+3² +3³+...+3²⁰¹² có chia hết cho 120 không ? vì sao

 

Answer 1

\(3+3^2+3^3+...+3^{2012}\)

\(=\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{2009}+3^{2010}+3^{2011}+3^{2012}\right)\)
\(=\left(3+3^2+3^3+3^4\right)+3.\left(3+3^2+3^3+3^4\right)+...+3^{2008}\left(3+3^2+3^3+3^4\right)\)

mà \(3+3^2+3^3+3^4=3+9+27+81=120⋮120\)

\(\Rightarrow\hept{\begin{cases}3+3^2+3^3+3^4⋮120\\3\left(3+3^2+3^3+3^4\right)⋮120\\3^{2008}\left(3+3^2+3^3+3^4\right)⋮120\end{cases}.......}\)

\(\Rightarrow3+3^2+3^3+...+3^{2012}⋮120\)

Answer 2

OE YTEHOBYEOBYETEBETWTETERTVJFHRDS123452435UI573367367645747T47WP1S--DDF-

V

-]

34-9

c

?'3V-'-'

'

-'

V'

-'

'

-6'

3-'C-'

-'

V6-'

T-'

6-9369--959295-2===