Question

Cho A = 1 + 3 + 3² + 3³ +....+ 3²⁰¹² và B = 3²⁰¹³ : 2. Tính B - A

Answer 1

Ta có: 

\(A=1+3+3^2+...+3^{2012}\)

\(\Rightarrow3A=3+3^2+3^3+...+3^{2013}\)

\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{2013}\right)-\left(1+3+3^2+...+3^{2012}\right)\)

\(\Rightarrow2A=3^{2013}-1\)

\(\Rightarrow A=\left(3^{2013}-1\right):2\)

Do \(B=3^{2013}:2\)

\(\Rightarrow B-A=3^{2013}:2-\left(3^{2013}-1\right):2\)

\(\Rightarrow B-A=\left(3^{2013}-3^{2013}+1\right):2\)

\(\Rightarrow B-A=1:2=\frac{1}{2}\)

Vậy \(B-A=\frac{1}{2}\)