Question

Chứng minh rằng A = 3+3^3+3^5+3^7+3^9+...+3^2009. chia hết cho 13

Answer 1

\(A=3+3^3+3^5+...+3^{2005}+3^{2007}+3^{2009}\)

\(A=3\cdot\left(1+3^2+3^4\right)+...+3^{2005}\cdot\left(1+3^2+3^4\right)\)

\(A=3\cdot91+...+3^{2005}\cdot91\)

\(A=91\cdot\left(3+...+3^{2005}\right)\)

\(A=13\cdot7\cdot\left(3+...+3^{2005}\right)⋮13\left(đpcm\right)\)

Answer 2

A=3+3^3+3^5+....+3^2009 (1)

9A=3^3+3^5+3^7+...+3^2011 (2)

trừ vế với vế của (2) cho (1) 

9A-A=(3^3+3^5+...+3^2011)-(3+3^3+...+3^2009)

8A=3^2011-3

A=\(\frac{3^{2011}-3}{8}\)

Answer 3

mình nhầm rồi đừng tích sai nhé