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\(H=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{1}{100}\right)\)
\(\Leftrightarrow H=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\cdot\cdot\cdot\cdot\frac{99}{100}\)
\(\Leftrightarrow H=\frac{1.2.3.4.....99}{2.3.4.5.....100}\)
\(\Leftrightarrow H=\frac{1}{100}\)
a, 11 1/4-(2 5/7+5 1/4)
= 45/4-(19/7+21/4)
= 45/4-223/28
=23/7
b, (8 5/11+3 5/8)-3 5/11
=(93/11+29/8)-38/11
=1063/88-38/11
=69/8
a, =\(11\frac{1}{4}-2\frac{5}{7}-5\frac{1}{4}\)
\(=\left(11\frac{1}{4}-5\frac{1}{4}\right)-2\frac{5}{7}\)
\(=6-2\frac{5}{7}\)
\(=\frac{23}{7}\)
b, \(=8\frac{5}{11}+3\frac{5}{8}-3\frac{5}{11}\)
\(=\left(8\frac{5}{11}-3\frac{5}{11}\right)+3\frac{5}{8}\)
\(=5+3\frac{5}{8}\)
\(=\frac{69}{8}\)
\(\left(\frac{1}{2}-1\right):\left(\frac{1}{3}-1\right):\left(\frac{1}{4}-1\right):...:\left(\frac{1}{100}-1\right)\)
\(=\frac{-1}{2}:\frac{-2}{3}:\frac{-3}{4}:...:\frac{-98}{99}:\frac{-99}{100}\)
\(=\frac{-1\cdot3\cdot4\cdot...\cdot99\cdot100}{2\cdot\left(-2\right)\cdot\left(-3\right)\cdot...\cdot\left(-98\right)\cdot\left(-99\right)}\)
\(=\frac{\left(-1\right)^{99}\cdot100}{2\cdot\left(-2\right)}=\frac{-1\cdot100}{-4}=\frac{-100}{4}=-25\)
- P/s: Không chắc chắn nhé!
a) \(\left|x+\frac{1}{2}\right|=\frac{1}{3}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x+\frac{1}{2}=\frac{1}{3}\\x+\frac{1}{2}=-\frac{1}{3}\end{cases}}\) \(\Leftrightarrow\)\(\orbr{\begin{cases}x=-\frac{1}{6}\\x=-\frac{5}{6}\end{cases}}\)
Vậy....
b) \(\left|x-\frac{1}{2}\right|=\frac{1}{3}-\frac{1}{2}\)
\(\Leftrightarrow\)\(\left|x-\frac{1}{2}\right|=-\frac{1}{6}\) vô lí do \(\left|a\right|\ge0\)
Vậy pt vô nghiệm
c) \(\left|x+\frac{1}{3}\right|-4=-1\)
\(\Leftrightarrow\)\(\left|x+\frac{1}{3}\right|=3\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x+\frac{1}{3}=3\\x+\frac{1}{3}=-3\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{8}{3}\\x=-\frac{10}{3}\end{cases}}\)
Vậy..
d) \(\left|x-\frac{1}{5}\right|+\frac{1}{3}=\frac{1}{4}-\left|-\frac{3}{2}\right|\)
\(\Leftrightarrow\)\(\left|x-\frac{1}{5}\right|+\frac{1}{3}=-\frac{5}{4}\)
\(\Leftrightarrow\)\(\left|x-\frac{1}{5}\right|=-\frac{19}{12}\)vô lí do \(\left|a\right|\ge0\)với mọi a
Vậy pt vô nghiệm
e) \(\left|x-\frac{5}{2}\right|=\frac{4}{3}-\left(\frac{2}{3}-\frac{1}{2}\right)\)
\(\Leftrightarrow\)\(\left|x-\frac{5}{2}\right|=\frac{7}{6}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x-\frac{5}{2}=\frac{7}{6}\\x-\frac{5}{2}=-\frac{7}{6}\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=3\frac{2}{3}\\x=\frac{4}{3}\end{cases}}\)
Vậy...