Question

Cho A = 3 + 3 \(^2\) + 3\(^3\) + 3\(^4\) +...+ 3\(^{120}\) 

Chứng minh rằng :

a, A chia hết cho 12

b, A chia hết cho 13

c, A chia hết cho 40

 

Answer 1

b, A = 3+3^2 +3^3 +3^4 +....+3^120 =﴾3+3^2+3^3﴿+......+﴾3^118+3^119+3^120﴿ =3﴾1+3+3^2﴿+....+3^118﴾1+3+3^2﴿ = 3.13+...+3^118. 13 = 13﴾ 3+...+3^118﴿ chia hết cho 13 c, A = 3+3^2 +3^3 + 3^4 +....+3^120 = ﴾3+3^2+3^3+3^4﴿+.....+﴾3^117+3^118+3^119+3^120﴿ = 3﴾1+3+3^2+3^3﴿ +...+3^117﴾ 1+3+3^2 +3^3﴿ = 3.40+ ...+3^117 .40 = 40 .﴾ 3+....+3^117﴿ chia hết cho 40

Answer 2

b, A = 3+3^2 +3^3 +3^4 +....+3^120

       =(3+3^2+3^3)+......+(3^118+3^119+3^120)

       =3(1+3+3^2)+....+3^118(1+3+3^2)

        = 3.13+...+3^118. 13

        = 13( 3+...+3^118) chia hết cho 13

c, A = 3+3^2 +3^3 + 3^4 +....+3^120

       = (3+3^2+3^3+3^4)+.....+(3^117+3^118+3^119+3^120)

       = 3(1+3+3^2+3^3) +...+3^117( 1+3+3^2 +3^3)

       = 3.40+ ...+3^117 .40

      = 40 .( 3+....+3^117) chia hết cho 40

Answer 3

a, 3+3^2+ 3^3 +....+3^119+3^120

= (3+3^2)+....+( 3^119+3^120)

= 3( 1+3) +....+3^119.( 1+3)

  = 3.4+....+3^119 . 4

  =4( 3+...+ 3^119) chia hết cho 4    

A= 3+3^2 +...+3^120

=3( 1+3 + 3^2 +....+3^119) chia hết cho 3  

mà 3 và 4 nguyên tố cùng nhau nên A chia hết cho 3 nhân 4

tức là a chia hết cho 12 ( điều phải chứng minh)

Answer 4

b, A = 3+3^2 +3^3 +3^4 +....+3^120        =﴾3+3^2+3^3﴿+......+﴾3^118+3^119+3^120﴿        =3﴾1+3+3^2﴿+....+3^118﴾1+3+3^2﴿         = 3.13+...+3^118. 13         = 13﴾ 3+...+3^118﴿ chia hết cho 13 c, A = 3+3^2 +3^3 + 3^4 +....+3^120        = ﴾3+3^2+3^3+3^4﴿+.....+﴾3^117+3^118+3^119+3^120﴿        = 3﴾1+3+3^2+3^3﴿ +...+3^117﴾ 1+3+3^2 +3^3﴿        = 3.40+ ...+3^117 .40       = 40 .﴾ 3+....+3^117﴿ chia hết cho 40

Answer 5

b, A = 3+3^2 +3^3 +3^4 +....+3^120        =﴾3+3^2+3^3﴿+......+﴾3^118+3^119+3^120﴿        =3﴾1+3+3^2﴿+....+3^118﴾1+3+3^2﴿         = 3.13+...+3^118. 13         = 13﴾ 3+...+3^118﴿ chia hết cho 13 c, A = 3+3^2 +3^3 + 3^4 +....+3^120        = ﴾3+3^2+3^3+3^4﴿+.....+﴾3^117+3^118+3^119+3^120﴿        = 3﴾1+3+3^2+3^3﴿ +...+3^117﴾ 1+3+3^2 +3^3﴿        = 3.40+ ...+3^117 .40       = 40 .﴾ 3+....+3^117﴿ chia hết cho 40