Question

A=1+3+3²+3³+...+3²⁰             .   B=3²¹:2    .TÍNH B-A

Answer 1

\(3A=3+3^2+3^3+3^4+...+3^{21}\)

\(\Rightarrow2A=3A-A=3^{21}-1\)

\(\Rightarrow A=\frac{3^{21}-1}{2}\)

Do đó \(B-A=\frac{3^{21}}{2}-\frac{3^{21}-1}{2}=\frac{3^{21}-\left(3^{21}-1\right)}{2}=\frac{1}{2}\)

Answer 2

\(A=1+3+3^2+3^3+...+3^{20}\)

\(\Rightarrow3A=3+3^2+3^3+...+3^{21}\)

\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{21}\right)-\left(1+3+3^2+3^3+...+3^{20}\right)\)

\(\Rightarrow2A=3^{21}-1\)

\(\Rightarrow A=\frac{3^{21}-1}{2}=\frac{3^{21}}{2}-\frac{1}{2}\)

Ta lại có: 

\(B=\frac{3^{21}}{2}\)

\(\Rightarrow B-A=\left(\frac{3^{21}}{2}-\frac{1}{2}\right)-\frac{3^{21}}{2}=\frac{1}{2}\)