Question

Tính giá trị biểu thức sau:

1+1/3+1/9+1/27+.....+1/729x3

Ai làm đúng mình chọn cho

 

Answer 1

\(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{729.3}\)

\(A=1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

=> \(3A=3+1+\frac{1}{3^1}+\frac{1}{3^2}+...+\frac{1}{3^6}\)

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

<=> \(2A=3-\frac{1}{3^7}=\frac{3^8-1}{3^7}\)

=> \(A=\frac{3^8-1}{2.3^7}\)