Nhân vế với vế , ta được :
\(3A=3.\left(\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(\Rightarrow3A=1+\frac{1}{3^1}+\frac{1}{3^2}+....+\frac{1}{3^{99}}\)
Lấy biểu thức 3A - A , ta được :
\(3A-A=\left(1+\frac{1}{3^1}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(\Rightarrow2A=1-\frac{1}{3^{100}}\)
\(\Rightarrow A=\left(1-\frac{1}{3^{100}}\right):2\)
A=1/3+1/3^2+...+1/3^100
=>3A=1+1/3+...+1/3^99
=>3A-A=(1+1/3+..+1/3^99)-(1/3+1/3^2+...+1/3^100)
=>2A=1-1/3^100
=>A=(1-1/3^100)/2
