Question

Cho A = 3+3^2+3^3+3^4+...+3^100

Chung minh rang A chia het cho 40

Answer 1

 ĐẶt A=3+3^2+3^3+....+3^100

 A= 3(1+3+3^2+3^3) +3^5(1+3+3^2+3^3)+...... + 3^97 ( 1 + 3 + 3^2 + 3^3)
A=3.40 +3^5.40+.....+3^97.40 

Vì 40 chia hết cho 40 => 3.40 +3^5.40+.....+3^97.40 
Vậy A chia hết cho 40. 

Answer 2

A=3+3²+3³+3⁴+...+3¹⁰⁰ chia hết cho 40

A=(3+3²+3³+3⁴)+(3⁵+3⁶+3⁷+3⁸)+...+(3⁹⁷+3⁹⁸+3⁹⁹+3¹⁰⁰)

A=3.(1+3+3²+3³)+3⁵.(1+3+3²+3³)+...+3⁹⁷.(1+3+3²+3³)

A=3.40+3⁵.40+...+3⁹⁷.40

A=40.(3+3⁵+...+3⁹⁷) chia hết cho 40 (đpcm)