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\(F=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right)...\left(1-\frac{1}{100}\right)\)
\(F=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{99}{100}\)
\(F=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{9.11}{10.10}\)
\(F=\frac{1.2.3.4...9}{2.3.4...10}.\frac{3.4.5...11}{2.3.4.5...10}\)
\(F=\frac{1}{10}.\frac{11}{2}=\frac{11}{21}\)
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 + 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 + 1/256 - 1/512
= 1 - 1/512
= 511/512
\(\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{9.11}\right).y=\frac{2}{3}\)
\(\Leftrightarrow2.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{9.11}\right).y=\frac{2}{3}\)
\(\Leftrightarrow2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right).y=\frac{2}{3}\)
\(\Leftrightarrow2.\left(1-\frac{1}{11}\right).y=\frac{2}{3}\)
\(\Leftrightarrow\frac{20}{11}.y=\frac{2}{3}\)
\(\Leftrightarrow y=\frac{11}{30}\)
Vậy ...
mình xem được kết quả đúng là 22/15 cơ bạn mình chỉ muốn biết cách giải đẻ ra 22/15 thôi
\(N=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{10^2}\)
\(N>\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)
\(N>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{11}=\frac{1}{2}-\frac{1}{11}=\frac{10}{22}>\frac{9}{22}\)
Vậy N > 9/22
a, \(5\cdot\left(4+6\cdot x\right)=290\Rightarrow4+6\cdot x=290:5\Rightarrow4+6\cdot x=58\)
\(\Rightarrow6\cdot x=58-4\Rightarrow6\cdot x=54\Rightarrow x=54:6\Rightarrow x=9\)
b, \(\left(15\cdot24-x\right):0,25=100:\frac{1}{4}\Rightarrow\left(15\cdot24-x\right):\frac{1}{4}=100:\frac{1}{4}\)
\(\Rightarrow\left(15\cdot24-x\right):\frac{1}{4}=100\cdot\frac{4}{1}\Rightarrow\left(15\cdot24-x\right):\frac{1}{4}=400\)
\(\Rightarrow15\cdot24-x=400\cdot\frac{1}{4}\Rightarrow15\cdot24-x=100\Rightarrow360-x=100\)
\(\Rightarrow x=360-100\Rightarrow x=260\)
= 1/2-1/3+1/3-1/4+1/4-1/5+.........+ 1/19-1/20
= 1/2-1/20
= 9/20
ok bn
B1 giải
quãng đường AB dài là:25.3=75(km)
vận tốc ô tô đó là:75 :1,5=50(km/giờ)
ĐS:50 km/giờ
B2
\(\frac{51}{50}+9\%+\frac{41}{100}+0,24=\frac{102}{100}+\frac{9}{100}+\frac{41}{100}+\frac{24}{100}=\left(\frac{9}{100}+\frac{41}{100}\right)+\left(\frac{51}{100}+\frac{24}{100}\right)\)
\(=\frac{50}{100}+\frac{75}{100}=\frac{125}{100}=\frac{5}{4}\)
\(F=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x...x\frac{99}{100}\)
\(F=\frac{1x3x2x4x3x5x4x6x...x9x11}{2x2x3x3x4x4x5x5x...x10x10}\)
\(F=\frac{1x2x3x3x4x4x5x5x...x9x9x10x11}{2x2x3x3x4x4x5x5x...x10x10}=\frac{11}{2x10}=\frac{11}{20}\)