Question

các bạn giúp mình nhé; Cho A=1+3+3 mũ 2 +3 mũ 3+......+3 mũ 59. Chứng tỏ A chia hát cho 4 và 13

Answer 1

\(A=1+3+3^2+...+3^{59}\\ =\left(1+3+3^2+3^3+3^4+3^5\right)+\left(3^6+3^7+3^8+3^9+3^{10}+3^{11}\right)+...+\left(3^{54}+3^{55}+3^{56}+3^{57}+3^{58}+3^{59}\right)\\ =1\left(1+3+3^2+3^3+3^4+3^5\right)+3^6\left(1+3+3^2+3^3+3^4+3^5\right)+...+3^{54}\left(1+3+3^2+3^3+3^4+3^5\right)\\ =\left(1+3+3^2+3^3+3^4+3^5\right)\left(1+3^6+...+3^{54}\right)\\ =364\left(1+3^6+...+3^{54}\right)\\ =4\cdot13\cdot7\left(1+3^6+...+3^{54}\right)\text{ chia hết cho 4 và 13}\)