Question

 

A = 3¹ ​+ 3⁴+ 3⁷+ ...+ 3¹⁰⁰

Chung minh A chia het cho 8

Cac ban oi giup minh nha minh can gap lam luon y,neu ai la GV thi giup em nha !

 

 

Answer 1

\(A=3^1+3^4+3^7+...+3^{100}\)

\(A=\left(3^1+3^4+3^7+3^{10}\right)+...+\left(3^{91}+3^{94}+3^{97}+3^{100}\right)\)

\(A=\left(3^1+3^4+3^7+3^{10}\right)+...+3^{96}.\left(3^1+3^4+3^7+3^{10}\right)\)

\(A=\left(3^1+3^4+3^7+3^{10}\right).\left(1+...+3^{96}\right)\)

\(A=61320.\left(1+...+3^{96}\right)\)

\(A=7665.8.\left(1+...+3^{96}\right)⋮8\)

\(​\Rightarrow A=3^1+3^4+3^7+...+3^{100}⋮8\)

Answer 2

C​ho hoi 3^​96 ​ o dau ra vay

Answer 3

Ukm tui cung ko bit 3⁹⁶ o dau lun a ra la 3⁹⁰