Question

Cho A=1+3+3 mũ 2 +3 mũ 3+......+3 mũ 59. Chứng tỏ A chia hết cho 40

Answer 1

\(A=\left(1+3+3^2+3^3\right)+...+\left(3^{56}+3^{57}+3^{58}+3^{59}\right)\\ A=\left(1+3+3^2+3^3\right)+...+3^{56}\left(1+3+3^2+3^3\right)\\ A=\left(1+3+3^2+3^3\right)\left(1+...+3^{56}\right)\\ A=40\left(1+...+3^{56}\right)⋮40\)

Answer 2

\(A=\left(1+3+3^2+3^3\right)+3^4\left(1+3+3^2+3^3\right)+...+3^{56}\left(1+3+3^2+3^3\right)\)

\(=40+3^4.40+...+3^{56}.40=40\left(1+3^4+...+3^{56}\right)⋮40\)

Answer 3

\(A=\left(1+3+3^2+3^3\right)+...+3^{56}\left(1+3+3^2+3^3\right)\)

\(=40\left(1+...+3^{56}\right)⋮40\)