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\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)
\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)
\(=\frac{1}{24}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)
\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)
\(=\frac{1}{10}\)
1)\(\frac{7}{8}>\frac{6}{7}>\frac{4}{5}>\frac{1}{2}>\frac{5}{16}\)
2)
a.\(\frac{3}{7}\)và\(\frac{5}{16}\)
Ta có :\(\frac{3}{7}=\frac{3\times5}{7\times5}=\frac{15}{35}\) \(\frac{5}{16}=\frac{5\times3}{16\times3}=\frac{15}{48}\)
\(\frac{15}{35}>\frac{15}{48}\Rightarrow\frac{3}{7}>\frac{5}{16}\)
b.làm tương tự như câu a nhé
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(A=1-\frac{1}{64}=\frac{63}{64}\)
Ta thấy: 1/2 = 1 - 1/2
1/2 + 1/4 = 3/4 = 1- 1/4
1/2 + 1/4 + 1/8 = 7/8 = 1 - 1/8
Tương tự ta có:
1/2 + 1/4 +1/8 + 1/16 + 1/32 + 1/64 = 1 - 1/64 = 63/64
\(\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{8}\right)-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{8}-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\)
b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)
3M=1+1/3+1/3^2+1/3^3+1/3^4
3M-M=1-1/3^5
2M=242/243
M=242/243*1/2=121/243
ta có : A=1/2+1/4+..+1/1024
=> A=1/21+1/22+..+1/210
=> A.2=(1/21+1/22+..+1/210).2
=> A.2=1+1/21+1/22+..+1/29
=> 2A-A=(1+1/21+1/22+..+1/29)-(1/21+1/22+..+1/210)
=> A=1-1/210
Tính nhanh:
\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\)\(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\)
\(=\left(\frac{1}{1}+\frac{1}{9}\right)+\left(\frac{1}{2}+\frac{1}{8}\right)\)\(+\left(\frac{1}{3}+\frac{1}{7}\right)+\left(\frac{1}{4}+\frac{1}{6}\right)+\frac{1}{5}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}\)
\(=\frac{4}{10}+\frac{2}{5}=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}\)
tks giúp mk nha! cảm ơn nhiều ạ...
Đặt \(A=2-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(=2-\frac{1}{9}=\frac{18}{9}-\frac{1}{9}=\frac{17}{9}\)