Question

chứng tỏ rắng C=1+ 3+3^2+.......+3^11 chia hết cho 40

Answer 1

\(C=1+3+3^2+....+3^{11}\)

\(C=\left(1+3+3^2+3^3\right)+\left(3^4+3^5+3^6+3^7\right)+\left(3^8+3^9+3^{10}+3^{11}\right)\)

\(C=40.1+40.3^4+40.3^8\)

\(C=40.\left(1+3^4+3^8\right)\)

CHia hết cho 40

Answer 2

C=1+3+3²+3³+...+3¹¹

=(1+3+3²+3³)+...+(3⁸+3⁹+3¹⁰+3¹¹)

=40+....+3⁸(1+3+3²+3³)

=40+...+3⁸.40=40(1+...+3⁸) chia hết cho 40

=>đpcm

Answer 3

C=(1+3+3^2+3^3)+(3^4+3^5+3^6+3^7)+(3^8+3^9+3^10+3^11)

  =40+40.3^4+40.3^8

  =40.(1+3^4+3^8) chia hết cho 40