Question

Bài 1:Chứng minh

3^1 + 3^2 + 3^3 + 3^4 +...+ 3^2009 + 3^2010) chia hết cho 13

Answer 1

goi tong la A 

A co so so hang la

(2010-1):1+1= 2010(so)

chia A thanh 670 nhom

A = (3^1+3^2+3^3)+....+(3^2008+3^2009+3^2010)

A = 3(1+3+3^2)+....+3^2008(1+3+3^2)

A = 3.13+.....+3^2008.13

A = 13.(3+...+3^2008)

Vi 13 chia het cho 13 => (3+...+3^2008)chia het cho 13

=> A chia het cho 13

 

Answer 2

3¹+3²+..........+3²⁰⁰⁹+3²⁰¹⁰

=(3+3²+3³)+.........+(3²⁰⁰⁸+3²⁰⁰⁹+3²⁰¹⁰)

=(3+3.3+3.3²)+.............+(3²⁰⁰⁸+3²⁰⁰⁸.3+3²⁰⁰⁸.3²)

=3(1+3+3²)+..........+3²⁰⁰⁸.(1+3+3²)

=3.13+.........+3²⁰⁰⁸.13

=(3+3³+............+3²⁰⁰⁸).3 chia hết cho 3

Answer 3

ta có:3^1+3^2+3^3+....+3^2010=(3^1+3^2+3^3)+(3^4+3^5+3^6)+...+(3^2008+3^2009+3^2010)=3^1(1+3+9)+3^4(1+3+9)+.....+3^2008(1+3+9)=3.13+3^4.13+...+3^2008.13=13.(3+3^4+...+3^2008)nên chia hết cho 13.vì vậy tổng trên chia hết cho 13