calibudaicho

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

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

\(C=40+3^4.40+3^8.40\)

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

Vậy C chia hết cho 40

C = ( 1 + 3 + 3² + 3³ ) + ( 3⁴ + 3⁵ + 3⁶ + 3⁷ ) + ( 3⁸ + 3⁹ + 3¹⁰ + 3¹¹ )

C = 40 + 3⁴ + 3⁸ . 40

C = 40 . ( 1 + 3⁴ + 3⁸ )

Vậy C chia hết cho 40

C=(1/2+1/3+....+1/2017+1/2018)/(1/2017+2/2016+.....+2016/2+2017/1)

tinh c giup minh huhu mai hoc roi :(((((

ta đảo  ngược A lại ta có 1+11²+11³+...+11⁹

2A=11²+11³+11⁴+....+11⁹+11¹⁰

lấy 2A-A còn 11¹⁰ có tận cùng băng 0 nên chia hết 5

\(C=\left(1+3+3^2+3^3\right)+...+\left(3^8+3^9+3^{10}+3^{11}\right)\)

\(C=\left(1+3+3^2+3^3\right)+...+3^8\left(1+3+3^2+3^3\right)\)

\(C=\left(1+3+3^2+3^3\right).\left(1+3^4+3^8\right)\)

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

Vậy \(C⋮40\)

sửa đề là cho \(C=1+3+3^2+3^3+...+3^{11}\)

Ta có: \(C=1+3+3^2+3^3+3^4+...+3^{11}\)

\(C=4+3^2\left(1+3\right)+3^4\left(1+3\right)+3^6\left(1+3\right)+...+3^{10}\left(1+3\right)\)

\(C=4+3^2.4+3^4.4+3^6.4+...+3^{10}.4\)

\(C=4\left(1+3^2+3^4+3^6+3^8+3^{10}\right)⋮4\left(ĐPCM\right)\)

VẬy C chia hết cho 4

Ta có: C=(\(1+3+3^2+3^3\))+.......+\(\left(3^8+3^9+3^{10}+3^{11}\right)\)

\(=40+.....+3^8\left(1+3+3^2+3^3\right)\)

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

Vậy \(C\)chia hết cho 40(Vì có chứa thừa số 40)