1. Tinh:
a) 1 + 1 phần 3 + 1 phần 9 + 1 phần 27 + 1 phần 81 = 81/81 + 27/81 + 9/81 + 3/81 + 1/81 = 121/81
đặt \(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(=1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\)
\(\Rightarrow3S=3+1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}\)
\(\Rightarrow3S-S=3-\frac{1}{3^4}\)
\(\Rightarrow2S=\frac{80}{81}\)
\(\Rightarrow S=\frac{\frac{80}{81}}{2}\)
\(=\frac{80}{162}\)
\(=\frac{40}{81}\)
\(a)1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(=\frac{81}{81}+\frac{27}{81}+\frac{9}{81}+\frac{3}{81}+\frac{1}{81}\)
\(=\frac{121}{81}\)
\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(=\frac{81}{81}+\frac{27}{81}+\frac{9}{81}+\frac{3}{81}+\frac{1}{81}\)
\(=\frac{81+27+9+3+1}{81}\)
\(=\frac{121}{81}\)
