Tính M \(\sqrt{1+1013^2+\frac{1013^2}{1014^2}}+\frac{1013}{1014}\)
Những câu hỏi liên quan
Cho \(A=\frac{1013}{1014}+\frac{1014}{1015}+\frac{1015}{1013}\)
So sanh A voi 3
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2. Cho:
B= 1 - 1/2 + 1/3 - 1/4 +...+ 1/2021 - 1/2022 + 1/2023 C= 1/1012 + 1/1013 + 1/1014 +...+ 1/2021 + 1/2022 + 1/2023
Tính: B-C
cho A=1/1.2+1/3.4+1/5.6+....+1/2021.2022 và B=1011+1010/1012+1009/1013+1008/1014+...+2/2020+1/2021 Chứng minh rằng : B/A là số nguyên
chứng minh đẳng thức: 10102+10133+10152+10162=10112+10122+10142+10172
chứng minh đẳng thức: 10102+10133+10152+10162=10112+10122+10142+10172
Tìm x biết:
\(\frac{x-2}{2015}+\frac{x-3}{2014}=\frac{x-1}{1013}\)
Mk sửa 1013 thành 1008 nhá
\(\frac{x-2}{2015}+\frac{x-3}{2014}=\frac{x-1}{1008}\)
\(\Leftrightarrow\frac{x-2}{2015}+\frac{x-3}{2014}-2=\frac{x-1}{1008}-2\)
\(\Leftrightarrow\left(\frac{x-2}{2015}-1\right)+\left(\frac{x-3}{2014}-1\right)=\frac{x-1}{1013}-2\)
\(\Leftrightarrow\frac{x-2-2015}{2015}+\frac{x-3-2014}{2014}=\frac{x-1-2016}{1008}\)
\(\Leftrightarrow\frac{x-2017}{2015}+\frac{x-2017}{2014}=\frac{x-2017}{1008}\)
\(\Leftrightarrow\frac{x-2017}{2015}+\frac{x-2017}{2014}-\frac{x-2017}{1008}=0\)
\(\Leftrightarrow\left(x-2017\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{1008}\right)=0\)
\(\Leftrightarrow x-2017=0\times\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{1008}\right)\)
\(\Leftrightarrow x-2017=0\)
\(\Leftrightarrow x=2017\)
Hok TOT ^_^
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So sánh P và Q, biết: \(P=\frac{1010}{1011}+\frac{1011}{1012}+\frac{1012}{1013}\) và \(Q=\frac{1010+1011+1012}{1011+1012+1013}\)
Ta có : Q=\(\frac{1010+1011+1012}{1011+1012+1013}\)=\(\frac{1010}{1011+1012+1013}+\frac{1011}{1011+1012+1013}+\frac{1012}{1011+1012+1013}\)
Vì1010/1011>1010/1011+1012+1013
1011/1012>1011/1011+1012+1013
1012/1013>1012/1011+1012+1013
=>P>Q
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Tìm x biết:
\(\frac{x-1}{2016}+\frac{x-2}{2015}-\frac{x-3}{2014}=\frac{x-4}{1013}\)
\(\frac{x-1}{2016}+\frac{x-2}{2015}-\frac{x-3}{2014}=\frac{x-4}{2013}\)
\(\left(\frac{x-1}{2016}-1\right)+\left(\frac{x-2}{2016}-1\right)-\left(\frac{x-3}{2014}-1\right)=\left(\frac{x-4}{2013}-1\right)\)
\(\frac{x-2017}{2016}+\frac{x-2017}{2015}-\frac{x-2017}{2014}=\frac{x-2017}{2013}\)
\(\frac{x-2017}{2016}+\frac{x-2017}{2015}+\frac{x-2017}{2014}-\frac{x-2017}{2013}=0\)
\(\left(x-2017\right)\left(\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2014}-\frac{1}{2013}\right)=0\)
\(x-2017=0\left(vì\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2014}-\frac{1}{2013}\ne0\right)\)
x=2017
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\(\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-\frac{1015}{1014}\right)\)
\(\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-\frac{1015}{1014}\right)\)
\(=\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-\frac{1014}{1014}\right).\left(1-\frac{1015}{1014}\right)\)
\(=\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-1\right).\left(1-\frac{1015}{1014}\right)\)
\(=\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...0.\left(1-\frac{1015}{1014}\right)\)
\(=0\)
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