Question

chứng minh :

\(B=3+3^2+3^3+3^4+..............+3^{100}\) CHIA HẾT CHO 4

 

Answer 1

\(B=3+3^2+3^3+...+3^{100}\)

\(=3\left(1+3\right)+3^3\left(1+3\right)+...+3^{99}\left(1+3\right)\)

\(=3.4+3^3.4+...+3^{99}.4\)

\(=4\left(3+3^3+...+3^{99}\right)⋮4\)

Answer 2

\(B=3+3^2+3^3+3^4+...+3^{99}+3^{100}\)

\(=3\left(1+3\right)+3^2\left(1+3\right)+...+3^{99}\left(1+3\right)\)

\(=\left(1+3\right)\left(3+3^2+...+3^{99}\right)\)

\(=4\left(3+3^2+...+3^{99}\right)\)⋮4

Answer 3

B = 3 + 3² + 3³ +\(3^4\)+ ... + \(3^{100}\)

B = (3 + 3²) + (3³ + 3⁴) + ... + (\(3^{99}\)+ \(3^{100}\)) 

B = 3(1 + 3) + 3³(1 + 3) + ...+ \(3^{99}\)(1 + 3)

B = 3.4 + 3³ . 4 + ... + \(3^{99}\) . 4

B = 4.(3 + 3³ + ... + \(3^{99}\)) ⋮ 4 

Vậy B⋮ 4

Nhớ xem lại nha