Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a.\(\left(\dfrac{1}{2}-\dfrac{3}{2x-5^2-5}\right)=11\)
b.\(\dfrac{2}{3}-\left|4x+\dfrac{1}{2}\right|=\dfrac{1}{2}\)
Đề là vậy đk bạn?
2,
Ta có : \(\left(x+5\right)⋮\left(x+1\right)\)
\(\Leftrightarrow\frac{x+5}{x+1}\in N\Leftrightarrow\frac{x+1+4}{x+1}=\frac{x+1}{x+1}+\frac{4}{x+1}=1+\frac{4}{x+1}\)
Vì \(1\in N\)
\(\Leftrightarrow\frac{4}{x+1}\in N\Leftrightarrow x+1\inƯ_4=\left\{1;2;4\right\}\)
\(\Rightarrow x=\left\{0;1;3\right\}\)
mỏi tay quá ~ bạn làm nốt 2 ý còn lại nha .
1,
Ta có : \(\left(x+2\right)⋮\left(x+1\right)\)
\(\Leftrightarrow\frac{x+2}{x+1}\in N\Leftrightarrow\frac{x+1+1}{x+1}=\frac{x+1}{x+1}+\frac{1}{x+1}=1+\frac{1}{x+1}\)
Vì \(1\in N\)
\(\Rightarrow\frac{1}{n+1}\in N\Leftrightarrow n+1\inƯ_1=\left\{1\right\}\).
\(\Rightarrow n=\left\{0\right\}\)
Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{9900}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)
\(=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{99x100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3_{ }}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\left(\frac{2}{3}x-\frac{1}{2}\right).\frac{3}{4}-\frac{2}{5}x=4\frac{1}{4}\)
\(\frac{1}{2}x-\frac{3}{8}-\frac{2}{5}x=4\frac{1}{4}\)
\(\frac{1}{10}x=\frac{17}{4}+\frac{3}{8}\)
\(\frac{1}{10}x=\frac{37}{8}\)
\(x=\frac{185}{4}\)
\(\left(\frac{2}{3}x-\frac{1}{2}\right).\frac{3}{4}-\frac{2}{5}x=4\frac{1}{4}\)
\(\frac{1}{2}x-\frac{3}{8}-\frac{2}{5}x=\frac{17}{4}\)
\(\frac{1}{2}x-\frac{2}{5}x=\frac{17}{4}+\frac{3}{8}\)
\(\frac{1}{10}x=\frac{37}{8}\)
\(x=\frac{37}{8}:\frac{1}{10}\)
\(x=\frac{185}{4}\)
\(A=\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{\left(2n\right)^2}< \frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{\left(2n-2\right).2n}\)
\(< \frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2n-2}-\frac{1}{2n}\right)\)
\(< \frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2n}\right)=\frac{1}{4}-\frac{1}{4n}< \frac{1}{4}\)
\(\Rightarrow\) \(A< \frac{1}{4}\)
Study well ! >_<
Đề thiếu
quên là <1/2