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Bạn kiểm tra lại đề hộ. Nếu có phân số \(\frac{1}{4}\)thì chịu còn không có thì dễ.
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt tổng trên là A . Ta có:
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
\(A=1-\frac{1}{1024}\)
\(A=\frac{1023}{1024}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,\\ \dfrac{3}{5}=\dfrac{21}{35};\dfrac{4}{7}=\dfrac{20}{35}\\ \dfrac{2}{3}=\dfrac{4}{6};\dfrac{5}{6}=\dfrac{5}{6}\\ \dfrac{4}{9}=\dfrac{8}{18};\dfrac{1}{6}=\dfrac{3}{18}\\ 2,\\ \dfrac{5}{9}=\dfrac{10}{18};\dfrac{7}{8}=\dfrac{14}{16};\dfrac{24}{42}=\dfrac{12}{21}\)
1. \(\dfrac{3}{5}=\dfrac{21}{35};\dfrac{4}{7}=\dfrac{20}{35}\)
\(\dfrac{2}{3}=\dfrac{4}{6};\dfrac{5}{6}=\dfrac{5}{6}\)
\(\dfrac{4}{9}=\dfrac{16}{36};\dfrac{1}{6}=\dfrac{6}{36}\)
2. \(\dfrac{5}{9}=\dfrac{10}{18}\)
\(\dfrac{7}{8}=\dfrac{14}{16}\)
\(\dfrac{24}{42}=\dfrac{12}{21}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(\dfrac{1}{1};\dfrac{1}{4};\dfrac{1}{9};\dfrac{1}{16};\dfrac{1}{19}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
a] 23/16
c)7/45
d)1/2
b)83/48
Đúng nhé mình làm tong toán nâng cao lớp 5 rồi
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{Đặt }S=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}.\)
\(\Rightarrow2S=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\)
\(\Rightarrow2S-S=S=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\right)\)
\(\Rightarrow S=1-\frac{1}{2048}=\frac{2047}{2048}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2 + 1/4 + 1/8 + 1/16 + 1/32
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32
=1-1/32
=31/32
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(=\frac{16}{32}+\frac{8}{32}+\frac{4}{32}+\frac{2}{32}+\frac{1}{32}\)
\(=\frac{16+8+4+2+1}{32}\)
\(=\frac{31}{32}\)
Vậy.......
nếu k quy đồng olaf k tính đc bn nhé
\(\text{Đặt A = }\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2\text{A}=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(2\text{A}-\text{A}=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(\text{A}=1-\frac{1}{32}=\frac{31}{32}\)