Question

b/chứng minh rằng : B=1+3+3²+...+3⁹⁹ chia hết cho  40

a/ viết các tổng sau thành thành 1 tích 3⁴+3⁵+3⁶+3⁷

Answer 1

a)  \(B=1+3+3^2+3^3+....+3^{99}\)

\(=\left(1+3+3^2+3^3\right)+\left(3^4+3^5+3^6+3^7\right)+...+\left(3^{96}+3^{97}+3^{98}+3^{99}\right)\)

\(=\left(1+3+3^2+3^3\right)+3^4\left(1+3+3^2+2^3\right)+....+3^{96}\left(1+3+3^2+3^3\right)\)

\(=\left(1+3+3^2+3^3\right)\left(1+3^4+...+3^{96}\right)\)

\(=40\left(1+3^4+....+3^{96}\right)\)\(⋮\)\(40\)

b)  \(3^4+3^5+3^6+3^7=3^4\left(1+3+3^2+3^3\right)=40.3^4\)