Question

[Hóa Lê thị]

[ 100/3 ] + [ 100/3^2 ] + [100/3^3 ] + [ 100/3^4 ]

GIUP MIK NHA

Answer 1

[Khanh Nguyễn Ngọc]

\(A=\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}+\frac{100}{3^4}\)

\(\Rightarrow3A=100+\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}\)

\(\Rightarrow3A-A=100+\left(\frac{100}{3}-\frac{100}{3}\right)+\left(\frac{100}{3^2}-\frac{100}{3^2}\right)+\left(\frac{100}{3^3}-\frac{100}{3^2}\right)-\frac{100}{3^4}\)

\(\Rightarrow2A=100-\frac{100}{3^4}=100.\left(1-\frac{1}{3^4}\right)=100.\frac{80}{81}\)

\(\Rightarrow A=\frac{100.80}{2.81}=\frac{4000}{81}\)