CMR
A=\(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+.......+\frac{1}{64}>1\)
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CMR
A=\(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+.....+\frac{1}{64}>1\)
thúy ơi dễ nhưng có biết làm ko vậy
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Bài: Tính:Pfrac{1}{99}-frac{1}{99.98}-frac{1}{98.97}-...-frac{1}{2.1}.Mfrac{3}{2}+frac{5}{4}+frac{9}{8}+frac{17}{16}+frac{33}{32}+frac{65}{64}-7Qfrac{1}{2}+frac{1}{4}+frac{1}{8}+...+frac{1}{64}Efrac{1}{2}+frac{1}{4}+frac{1}{6}+frac{1}{8}+frac{1}{10}+frac{1}{12}Ffrac{1}{2.5}+frac{1}{5.8}+frac{1}{8.11}+...+frac{1}{62.65}
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Bài: Tính:
P=\(\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{2.1}\).
M=\(\frac{3}{2}+\frac{5}{4}+\frac{9}{8}+\frac{17}{16}+\frac{33}{32}+\frac{65}{64}-7\)
Q=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{64}\)
E=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\)
F=\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{62.65}\)
\(P=...\)
\(=\frac{1}{99}-\frac{1}{99}+\frac{1}{98}-\frac{1}{98}+\frac{1}{97}-...-\frac{1}{2}+1\)
\(=\frac{1}{99}-1=\frac{-98}{99}\)
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\(M=...\)
\(=\frac{2}{2}+\frac{1}{2}+\frac{4}{4}+\frac{1}{4}+...+\frac{64}{64}+\frac{1}{64}-7\)
\(=1+1+1+1+1+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}-7\)
\(=\frac{1+2+2^2+2^3+2^4+2^5}{2^6}-1\)
\(=\frac{2^6-1}{2^6}-1=1-\frac{1}{2^6}-1=-\frac{1}{2^6}\)
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Tìm x
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{9}{10}.....\frac{36}{62}.\frac{31}{64}=\frac{1}{2^x}\)
1/4 . 2/6 . 3/8 . ... .30/62 .31/64 = 2^x
(1/2 . 1/2).(2/3 . 1/2).(3/4 . 1/2). ... .(30/31 . 1/2).(31/32 . 1/2) = 2^x
(1/2.1/2. ... .1/2).(1/2 . 2/3 . 3/4. ... .30/31 . 31/32) = 2^x
(31 số 1/2)
(1/2)^31. = 2^x
=> 0=x+36
x=0-36
x=-36
Vậy x=-36
Theo mk nghĩ,mk làm đúng nha .Tk cho mk
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Để mk sửa phần này một chút
\((\frac{1}{2})^{31}\cdot\frac{1\cdot2\cdot3.....30\cdot31}{2\cdot3\cdot4.....31\cdot32}=2^x\)
\(\frac{1^{31}}{2^{31}}\cdot\frac{1}{32}=2^x\)
\(\frac{1}{2^{31}}\cdot\frac{1}{2^5}=2^x\)
\(\frac{1}{2^{36}}=2^x\)
\(1=2^x\cdot2^{36}\)
\(2^0=2^x+36\)
Rồi bn tự suy luận nha
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\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.........................\frac{31}{64}=\frac{1}{2^x}\)
Có 31 thừa số
\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}\right)...................\left(\frac{1}{2}.\frac{31}{32}\right)=\frac{1}{2^x}\)
\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}...............\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}...............\frac{31}{32}\right)=\frac{1}{2^x}\)
Có 31 thừa số Có 31 thừa số
\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1.2....................31}{2.3..............32}=\frac{1}{2^x}\)
\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{32}=\frac{1}{2^x}\)
\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{2^5}=\frac{1}{2^x}\)
\(\Leftrightarrow\frac{1}{2^{36}}=\frac{1}{2^x}\)
\(\Leftrightarrow x=36\)
Vậy x=36
Chúc bạn học tốt
Tính
a) \(\frac{1}{5}+\frac{-1}{6}+\frac{1}{7}+\frac{1}{-8}+\frac{1}{9}+\frac{1}{8}+\frac{1}{-7}+\frac{-1}{6}+\frac{-1}{5}\)
b) (-11).36-64.11
c) \(\frac{\frac{1}{3}+\frac{1}{7}+\frac{1}{13}}{\frac{2}{3}+\frac{2}{7}+\frac{2}{13}}.\frac{\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\frac{3}{256}}{1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}}+\frac{3}{8}\)
Chứng tỏ rằng :Afrac{1}{2}-frac{1}{4}+frac{1}{8}-frac{1}{16}+frac{1}{32}-frac{1}{64} frac{1}{3}Bfrac{1}{5}+frac{1}{9}+frac{1}{10}+frac{1}{41}+frac{1}{42} frac{1}{2}Please help me if you know!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!I need answer!!!!!!!!!!!!!!!!!!
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Chứng tỏ rằng :
A=\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\) < \(\frac{1}{3}\)
B=\(\frac{1}{5}+\frac{1}{9}+\frac{1}{10}+\frac{1}{41}+\frac{1}{42}< \frac{1}{2}\)
Please help me if you know!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I need answer!!!!!!!!!!!!!!!!!!
\(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\)
\(2A=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\)
\(2A+A=\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\right)+\left(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\right)\)
\(3A=1-\frac{1}{64}\)
\(3A=\frac{63}{64}\Rightarrow A=\frac{63}{64}\div3=\frac{21}{64}< \frac{1}{3}\)
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\(\frac{10+\frac{9}{2}+\frac{8}{3}+\frac{7}{4}+ \frac{6}{5}+\frac{5}{6}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}+\frac{1}{11}}\)
24 tháng 9 2016 lúc 9:59
a) \(\left(-\frac{40}{51}\cdot0,32\cdot\frac{17}{20}\right):\frac{64}{75}\)
b) \(-\frac{10}{11}\cdot\frac{8}{9}+\frac{7}{18}\cdot\frac{10}{11}\)
c) \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{11}{28}+\frac{29}{42}:\frac{1}{28}-8\)
a ) \(\left(-\frac{40}{51}.0,32.\frac{17}{20}\right):\frac{64}{75}\)
\(=\left(-\frac{40}{51}.\frac{8}{25}.\frac{17}{20}\right):\frac{64}{75}\)
\(=\left(\frac{-40.8.17}{51.25.20}\right):\frac{64}{75}\)
\(=\left(\frac{-16}{75}\right).\frac{75}{64}\)
\(=\frac{-1}{1}.\frac{1}{4}=-\frac{1}{4}\)
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\(\frac{10+\frac{9}{2}+\frac{8}{3}+\frac{7}{4}+ \frac{6}{5}+\frac{5}{6}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}+\frac{1}{11}}\)
\(\frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}}{\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}}=?\)