Gọi giá trị của biểu thức trên là A. Ta có:
\(A=\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}\)
\(3A=\dfrac{15}{2}+\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}\)
\(3A-A=\left(\dfrac{15}{2}+\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}\right)-\left(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}\right)\)
\(2A=\dfrac{15}{2}-\dfrac{5}{162}\)
\(A=\left(\dfrac{15}{2}-\dfrac{5}{162}\right)\div2=\dfrac{605}{81}\div2=\dfrac{605}{162}\)
= 10/3 + 5/18 + 5/54 + 5/162
= 65/18 + 5/54 + 5/162
= 100/27 + 5/162
= 605/162
\(\dfrac{5}{2}\)+\(\dfrac{5}{6}\)+\(\dfrac{5}{18}\)+\(\dfrac{5}{54}\)+\(\dfrac{5}{162}\)=\(\dfrac{605}{162}\)
=10/3 + 5/18 + 5/162
=65/18 + 5/54 + 5/162
=100/27 + 5/162
=605/162 nhé bn
