tổng các ps trên là ; \(\frac{364}{729}\)

đặt biểu thức đó là X

ta có :

\(3X=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(\Rightarrow3X-X=1-\frac{1}{729}\)

\(\Rightarrow X=\frac{728}{729}.\frac{1}{2}=\frac{364}{729}\)

Đặt A=1/3 + 1/9 + 1/27 + 1/81 + 1/24 + 1/729

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\)

\(3A=3\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)\)

\(3A=1+\frac{1}{3}+...+\frac{1}{3^5}\)

\(3A-A=\left(1+\frac{1}{3}+...+\frac{1}{3^5}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)\)

\(2A=1-\frac{1}{3^6}\)

\(A=\frac{1-\frac{1}{3^6}}{2}\)

hâm ak giải cách tiểu học cho tui dễ hiểu !!!

\(b,\)Đặt \(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37\cdot38\cdot39}\)

\(B=\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{37.38\cdot38}\)

\(2B=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{37.38}-\frac{1}{38.39}\)

\(2B=\frac{1}{1.2}-\frac{1}{38.39}\)

\(\Rightarrow B=\frac{\left(\frac{1}{1.2}-\frac{1}{38.39}\right)}{2}=\frac{185}{741}\)

⇒B =
2
1.2
1 −
38.39
1
=
741
( ) 18

A=\(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{243}+\frac{1}{729}\)

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^5}+\frac{1}{3^6}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^4}+\frac{1}{3^5}\)

Lấy 3A - A ta được : (\(1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^4}+\frac{1}{3^5}\) ) - (\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^5}+\frac{1}{3^6}\))

2A = 1 - \(\frac{1}{3^6}\)

=> A = \(\frac{1-\frac{1}{3^6}}{2}=\frac{364}{729}\)