Question

[Tiến Chu]

Chứng Tỏ Rằng:

c, 5+5²+5³+...+5⁹⁶chia hết cho 126

e, 2+2²+2³+2⁴+...+2²⁰⁰chia hết cho 3 ; 15

Answer 1

[Nguyễn Minh Quang]

ta có: 

Answer 2

[༺༒༻²ᵏ⁸]

\(c,\text{Đ}\text{ặt}:A=5+5^2+5^3+...+5^{96}\)

\(A=\left(5+5^2+5^3\right)+....+\left(5^{94}+5^{95}+5^{96}\right)\)

\(A=5\left(1+5+5^2\right)+...+5^{94}\left(1+5+5^2\right)\)

\(A=5.126+...+5^{94}.126\)

\(A=126\left(5+5^4+...+5^{94}\right)\)

\(M\text{à}:A=126\left(5+5^4+...+5^{94}\right)⋮126\)

\(\Rightarrow5+5^2+5^3+...+5^{96}⋮126\)