80/81

80/81

80/81 nhe ban

Đặt A là kết quả, ta có:
3A = 3 x (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729
= 1 - 1/729
A x 2 = 728/729
A = 364/729
 

\(A=\frac{1}{2\cdot15}+\frac{3}{11\cdot2}+\frac{4}{1\cdot11}+\frac{5}{2\cdot1}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{7\cdot2\cdot15}+\frac{3}{11\cdot2\cdot7}+\frac{4}{7\cdot1\cdot11}+\frac{5}{2\cdot7\cdot1}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{15\cdot14}+\frac{3}{14\cdot11}+\frac{4}{11\cdot7}+\frac{5}{7\cdot2}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{14}-\frac{1}{15}+\frac{1}{14}-\frac{1}{11}+\frac{1}{11}-\frac{1}{7}+\frac{1}{7}-\frac{1}{5}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{14}-\frac{1}{5}=\frac{5}{70}-\frac{14}{70}=\frac{-9}{70}\Rightarrow A=\frac{-9}{70}:\frac{1}{7}=\frac{-9\cdot7}{1\cdot70}\)\(=\frac{-9\cdot7}{10\cdot7}=\frac{-9}{10}\)

cho bieu thuc: P=(1/1.2+1/3.4+1/5.6+...+1/59.60).31.32.33.....59.60 Chung minh rang P chia het cho 91

1+1/3+1/9+1/27+1/81 (ko quy đồng nha) 

Không quy đồng 

Ta có : \(1+\frac{1}{3}-\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)

ta có : \(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)

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

\(\Rightarrow3A=3+1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\)

\(\Rightarrow3A-A=\left(3+1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\right)\)

\(\Rightarrow2A=3-\frac{1}{3^4}\)

\(\Rightarrow A=\left(3-\frac{1}{3^4}\right):2=\frac{121}{81}\)

bai kho qua

A: 3/4 < 4/5      B:4/3 > 1999/1998

Chúc bạn học giỏi ! nhớ k cho mình nhé !

Ta có : 1 - 13/27 = 14/27

           1 - 27/41 = 14/41

Vì 14/27 > 14/41 nên 13/27 < 27/41

1-13/27=14/27

1-27/41=14/41

vi 14/27>14/41 nen 13/27 > 27/41 

**** mik nha 

Ta đặt:  A = \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)

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

\(\Rightarrow3A=3+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\)

\(\Rightarrow3A-A=\left(3+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\right)\)

\(\Rightarrow2A=3-\frac{1}{3^4}\)

\(\Rightarrow A=\left(3-\frac{1}{3^4}\right):2\)

Giải 
1+ 1 /3+1/9+1/27+1/81+1/243+1/729. 
Đặt: 
S = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 
Nhân S với 3 ta có: 
S x 3 = 3 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 
Vậy: 
S x 3 - S = 3 - 1/243 
2S = 2186 / 729 
S = 2186 / 729 : 2 
S = 1093/729