Question

bài 3

1. So sánh

A = 1+3+3²+3³+3⁴+3⁵+3⁶

và

B = 3⁷ - 1

Answer 1

\(A=1+3+3^2+3^3+3^4+3^5+3^6\)

\(3A=3\left(1+3+3^2+3^3+3^4+3^5+3^6\right)\)

\(3A=3+3^2+3^3+3^4+3^5+3^6+3^7\)

\(3A-A=\left(3+3^2+3^3+3^4+3^5+3^6+3^7\right)-\left(1+3+3^2+3^3+3^4+3^5+3^6\right)\)

\(\Rightarrow2A=3^7-1\)

\(A=\dfrac{3^7-1}{2}\)

\(A< 3^7-1\)

Answer 2

Biến đổi vế A ta có

\(A=\)\(1+3+3^2+3^3+3^4+3^5+3^6\)

\(3\)\(A=3.\left(1+3+3^2+3^3+3^{\text{4}}+3^{\text{5}}+3^6\right)\)

\(3\)\(A=3+3^2+3^3+3^4+3^5+3^6+3^7\)

\(3A-A=\left(3+3^2+3^3+...+3^7\right)-\left(1+3+3^2+3^3+...+3^6\right)\)\(2A=3^7-1\)

\(A=\dfrac{3^7-1}{2}\)

bạn tick cho mik nhé !!! mà cậu sai đề bài hay sao ý phải là B=\(\dfrac{3^7-1}{2}\) thui cậu tự so sánh nhé