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\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}+\frac{1}{1536}\)
\(A\times2=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}+\frac{2}{384}+\frac{2}{768}+\frac{2}{1536}\)
Rút gọn ta được
\(A\times2=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}\)
\(A\times2-A=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{768}-\left[\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1536}\right]\)
\(A=\frac{2}{3}+\frac{1}{3}-\frac{1}{3}-\frac{1}{1536}\)
\(A=\frac{2}{3}-\frac{1}{1536}=\frac{341}{512}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
e quy đồng ra nháp rồi cộng các số phù hợp là ra kết quả
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\(=2\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{192}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{192}\right)\)
\(=2\left(1-\frac{1}{192}\right)\)
\(=2\times\frac{191}{192}\)
\(=\frac{191}{96}\)
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MSC:192
\(\frac{4}{3}+\frac{1}{3}+\frac{1}{12}+\frac{1}{48}+\frac{1}{192}\)
\(=\frac{256}{192}+\frac{64}{192}+\frac{16}{192}+\frac{4}{192}+\frac{1}{192}\)
\(=\frac{341}{192}\)
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\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
= \(\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{12}+\frac{1}{24}\right)+\left(\frac{1}{48}+\frac{1}{96}\right)+\frac{1}{192}\)
= \(\left(\frac{1}{2}+\frac{1}{8}\right)+\left(\frac{1}{32}+\frac{1}{192}\right)\)
= \(\frac{5}{8}+\frac{1}{192}\)
= \(\frac{121}{192}\)
tính nhanh hộ mình câu này với :
\(\frac{4}{3}+\frac{1}{3}+\frac{1}{12}+\frac{1}{48}+\frac{1}{192}\)
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= 1 - 4/3 + 1/3 - 1/3 + 1/12 - 1/12 + 1/48 - 1/48 + 1/92
= 1 + 1/92
= 92/92 + 1/92
= 93/92
Ko biết có đúng không nữa!
\(\frac{4}{3}+\frac{1}{3}+\frac{1}{3x4}+\frac{1}{3x4^2}+\frac{1}{3x4^3}=\frac{4^4+1x4^3+1x4^2+1x4+1}{3x4^3}.\)
\(=\frac{256+64+16+4+1}{3x4^3}=\frac{341}{192}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
cái a bằng 1962
cái b bằng 127/192
à quên mình chưa rút gọn phân số đấy đâu bạn ạ
ban rút gọn phân số đấy hộ mình nha
![](https://rs.olm.vn/images/avt/0.png?1311)
4/795