Đặt :
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...................+\dfrac{1}{3^{2016}}\)
\(3A=3\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...............+\dfrac{1}{3^{2016}}\right)\)
\(3A=\dfrac{3}{3}+\dfrac{3}{3^2}+\dfrac{3}{3^3}+.................+\dfrac{3}{3^{2016}}\)
\(3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+......................+\dfrac{1}{3^{2015}}\)
\(3A-A=\left(1+\dfrac{1}{3}+\dfrac{1}{3^2}+..............+\dfrac{1}{3^{2015}}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+.............+\dfrac{1}{3^{2016}}\right)\)
\(A=1-\dfrac{1}{3^{2016}}\)
\(A=\dfrac{3^{2016}-1}{3^{2016}}\)
~~ Chúc bn học tốt ~~
Đặt :
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2016}}\)
\(\dfrac{1}{3}A=\dfrac{1}{3}.\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2016}}\right)\)
\(\dfrac{1}{3}A=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2017}}\)
\(\dfrac{1}{3}A-A=\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2017}}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2016}}\right)\)
\(-\dfrac{2}{3}A=\dfrac{1}{3^{2017}}-\dfrac{1}{3}\)
\(A=\dfrac{\dfrac{1}{3^{2017}}-\dfrac{1}{3}}{-\dfrac{2}{3}}\).
