Question

Chung minh :

 \(A=3+3^2+3^3+3^4+...+3^{25}\)Khong chia het cho 39 

 1) Cac ban oi , may mk ko viet dc tieng Viet , cac ban thong cam !!

2) Mk thay bai nay sao sao ay , khi nhom 3 chu so dau tien thi van chia het cho 39 ma ! Ai co cach giai naof hay ko ?? Giup mk voi ak !!

HELP ME , PLEASE !!!!! ^^

Answer 1

Ta có : \(A=3+3^2+3^3+3^4+...+3^{25}\)

\(=3+\left(3^2+3^3+3^4\right)+...+\left(3^{23}+3^{24}+3^{25}\right)\)

\(=3+3\left(3+3^2+3^3\right)+...+3^{22}\left(3+3^2+3^3\right)\)

\(=3+3.39+...+3^{22}.39\)

\(=3+39\left(3+...+3^{22}\right)\)

\(\Rightarrow A\)chia cho 39 dư 3

\(\Rightarrow A\)không chia hết cho 39 ( đpcm )

Answer 2

Cảm ơn bạn rất rất nhiều !! Mk kcho bạn rồi đó

Answer 3

Ta có

3+3^2+3^3+....+3^25

=3+(3^2+3^3+3^4)+.....+(3^23+3^24+3^25)

=3+3(3+3^2+3^3)+.......+3^22(3+3^2+3^3)

=3+3.39+....+3^22.39

=3+39(3+3^4+....+3^22) chia 39 dư 3

=> đpcm