Question

tính bằng cách thuận tiện nhất 1/3+1/9+1/27+1/81+1/243

Answer 1

\(A=\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{243}\)

=>3A=1+1/3+...+1/81

=>2A=1-1/243=242/243

=>A=121/243

Answer 2

Answer 3

\(3A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}\\ 3A-A=\left(1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\right)\\ 2A=1-\dfrac{1}{243}\\ 2A=\dfrac{242}{243}\\ A=\dfrac{242}{243}:2=\dfrac{121}{243}\)