Question

*Tính nhanh:

A = 1/3+ 1/3(mũ 2) +1/3(mũ 3)+.....+1/3(mũ 8)

Answer 1

A=\(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^8}\)

A.3=\(3\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^8}\right)\)

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

A.3-A=\(\left(1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^7}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^8}\right)\)

A.2=\(1-\dfrac{1}{3^8}\)

A=\(\dfrac{1-\dfrac{1}{3^8}}{2}=\dfrac{3280}{6561}\)

Answer 2

Kết quả : \(\dfrac{3316}{6561}\)