\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{768}+\frac{1}{1536}\)
Tính nhanh :
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{1536}+\frac{1}{3072}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{1536}+\frac{1}{3072}\)
\(=\frac{2}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{12}+\frac{1}{12}-\frac{1}{24}+...+\frac{1}{1536}-\frac{1}{3072}\)
\(=\frac{2}{3}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+\left(\frac{1}{12}-\frac{1}{12}\right)+...+\left(\frac{1}{1536}-\frac{1}{1536}\right)-\frac{1}{3072}\)
\(=\frac{2}{3}-\frac{1}{3072}\)
\(=\frac{2047}{3072}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{768}=x\)
,\(\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+............+\frac{1}{768}=???\)
Giúp mình với!!! Thankyou nhiều ^_^
Thank nha!!! nhờ bạn mik được 10 điểm
G = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1536}\)
Kết quả của phép tính
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+........+\frac{1}{768}\)
Tính A bằng :\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}...+\frac{1}{192}+\frac{1}{384}\).Tìm A?
A = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{192}+\frac{1}{384}\)
A x 2 =(1/2+1/6+1/12+1/24+…+1/192+1/384) x 2
A x 2 = 1 + 2/6 + 2/12 + 2/24 + ... + 2/192 + 2/384
Rút gọn ta được:
A x 2 = 1 + 1/3 + 1/6 + 1/12 + ... + 1/96 + 1/192
A x 2 - A = 1 + 1/3 + 1/6 + 1/12 + ... + 1/96 + 1/192 - (1/2+1/6+1/12+1/24+…+1/192+1/384)
A = 1 + 1/3 - 1/2 - 1/384
A = 5/6 - 1/384
A = 319/384
ĐS: 319/384 .
A = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+.......+\frac{1}{192}+\frac{1}{384}\)
A = \(\frac{1}{384}x128+\frac{1}{384}x64+\frac{1}{384}x32+.......+\frac{1}{384}x1\)
A = \(\frac{1}{384}x\left(128+64+32+16+8+4+2+1\right)\)
A = \(\frac{1}{384}x255\)
A = \(\frac{85}{128}\)
Cho :
\(A=\frac{19}{24}-\frac{1}{2}-\frac{1}{3}-\frac{7}{24}\)
\(B=\frac{7}{12}+\frac{5}{6}+\frac{1}{4}-\frac{3}{7}-\frac{5}{12}\)
a, Tính A và B
b, Tìm x biết A - x = B
a)
\(A=\left(\frac{19}{24}-\frac{7}{24}\right)-\left(\frac{1}{2}+\frac{1}{3}\right)\)
\(A=\frac{1}{2}-\frac{1}{2}+\frac{1}{3}\)
\(A=\frac{1}{3}\)
\(B=\left(\frac{7}{12}-\frac{5}{12}\right)+\left(\frac{5}{6}+\frac{1}{4}-\frac{3}{7}\right)\)
\(B=\left(\frac{1}{6}+\frac{5}{6}\right)+\frac{1}{4}-\frac{3}{7}\)
\(B=\frac{5}{4}-\frac{3}{7}\)
\(B=\frac{23}{28}\)
b)
\(x=A-B\)
\(x=\frac{1}{3}-\frac{23}{28}\)
\(x=\frac{-41}{84}\)
A=\(\left(\frac{19}{24}-\frac{7}{24}\right)+\left(-\frac{1}{2}-\frac{1}{3}\right)\)
A=\(\frac{1}{2}+-\frac{5}{6}\)=\(-\frac{1}{3}\)
B=\(\left(\frac{7}{12}+\frac{5}{6}+\frac{1}{4}-\frac{5}{12}\right)-\frac{3}{7}\)
B=\(\frac{5}{4}-\frac{3}{7}\)=\(\frac{23}{28}\)
A-x=B
(=)\(-\frac{1}{3}\)-x=\(\frac{23}{28}\)
(=)x=-97/84
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{96}.Tinh\)
Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{96}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+.....+\frac{1}{192}\)
\(\Rightarrow A-\frac{1}{2}A=\frac{1}{3}-\frac{1}{192}\)
\(\Rightarrow\frac{1}{2}A=\frac{21}{64}\)
\(\Rightarrow A=\frac{21}{64}.2=\frac{21}{32}\)
Cậu nên nhớ máy móc : chỉ cần lấy 1 - 1/96 là ra ngay kết quả
Và kết quả = 95/96
Cách này luôn luôn ĐÚNG !!
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(A+\frac{1}{96}=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{96}\)
\(A+\frac{1}{96}=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{48}\)
\(A+\frac{1}{96}=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{24}\)
...
\(A+\frac{1}{96}=\frac{1}{3}+\frac{1}{3}\Rightarrow A=\frac{2}{3}-\frac{1}{96}=\frac{2\cdot32-1}{96}=\frac{63}{96}=\frac{21}{32}\).