Question

[Ƹ̴Ӂ̴Ʒ εїзBest Friend Ƹ̴Ӂ̴Ʒ εїз]

Cho C = 3 + 3³ + 3⁵ + .... + 3¹⁹⁹¹ . Chứng minh rằng :

a ,C chia hết cho 13

b , C chia hết cho 41

c , C chia hết cho 40

làm câu nào cũng đc

Answer 1

[Nguyễn Minh Dương]

mk làm câu A = ... nha

ta có A = 3 + 3³ + 3⁵ + ...+3¹⁹⁹¹

A = ( 3 + 3³ + 3⁵ ) + ( 3⁷ + 3 ⁹ + 3¹¹ ) + ... + ( 3¹⁹⁸⁷  + 3^{1989 + 1991} )

A = 3 . (1 + 3 + 3² ) + 3⁷ . ( 1 + 3 + 3² ) + ... + 3¹⁹⁸⁷ . ( 1 + 3 + 3² )

A = 3 . 13 + 3⁷ . 13 + ... + 3¹⁹⁸⁷. 13

A = 13 . ( 3 + 3⁷ + ... + 3¹⁹⁸⁷ )   ( VÌ 13 CHIA HẾT CHO 13 )

=> A CHIA HẾT CHO 13

Answer 2

[Tẫn]

\(C=3+3^3+3^5+.....+3^{1991}.\)

\(=\left(3+3^3+3^5+3^7\right)+\left(3^9+3^{11}+3^{13}+3^{15}\right)+.....+\left(3^{1985}+3^{1987}+3^{1989}+3^{1991}\right)\)

\(=3.\left(1+3^2+3^4+3^6\right)+3^9\left(1+3^2+3^4+3^6\right)+....+3^{1985}\left(1+3^2+3^4+3^6\right)\)

\(=3.820+3^9.820+....+3^{1985}.820\)

\(=820\left(3+3^9+....+3^{1985}\right)\)

\(=41.20\left(3+3^9+...+3^{1985}\right)\)

\(\Rightarrow C⋮41\)