\(=\dfrac{45}{19}-\left(\dfrac{1}{2}+\left(\dfrac{1}{3}+4\right)^{-1}\right)^{-1}\)
\(=\dfrac{45}{19}-\left(\dfrac{1}{2}+\dfrac{3}{13}\right)^{-1}\)
\(=\dfrac{45}{19}-\dfrac{26}{19}=\dfrac{19}{19}=1\)
Thực hiện phép tính
a) A= \(1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)\)\(+\dfrac{1}{4}\left(1+2+3+4\right)+...+\dfrac{1}{2013}\left(1+2+...+2013\right)\)
b) B=\(\dfrac{1-3}{1.3}+\dfrac{2-4}{2.4}+\dfrac{3-5}{3.5}+\dfrac{4-6}{4.6}+...+\dfrac{2011-2013}{2011.2013}+\dfrac{2012-2014}{2012.2014}-\dfrac{2013+2014}{2013.2014}\)
Bài 1 : Thực hiện phép tính ( tính hợp lý nếu có thể )
a ) \(\dfrac{1}{12}+\dfrac{3}{4}\)
b ) \(\dfrac{-4}{7}.1\dfrac{1}{2}\)
c )\(\dfrac{7}{9}+\left(\dfrac{2}{3}+\dfrac{-7}{9}\right)\)
d )\(\dfrac{2}{3}-\dfrac{1}{3}:\dfrac{3}{4}\)
e )\(\dfrac{-7}{25}.\dfrac{11}{13}+\dfrac{-7}{25}.\dfrac{2}{13}\)
g )\(2\dfrac{2}{5}.0,25-\left(\dfrac{11}{20}+75\%\right):\dfrac{13}{5}\)
\(\left(\dfrac{1}{64}-\dfrac{1}{3^2}\right).\left(\dfrac{1}{64}-\dfrac{1}{4^2}\right).\left(\dfrac{1}{64}-\dfrac{1}{5^2}\right)...\left(\dfrac{1}{64}-\dfrac{1}{64^2}\right)\)
cho G = \(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{4}\right)\left(1+\dfrac{1}{16}\right)+\left(1+\dfrac{1}{256}\right)......\left(1+\dfrac{1}{2^{1024}}\right)\)và H = \(\dfrac{1}{2^{2047}}\)
Tính G + H
1.Tính nhanh:
A= \(\dfrac{\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}}{\dfrac{5}{12}+1-\dfrac{7}{11}}\)
2. Cho: B =\(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{19}\) .Hãy chứng tỏ rằng B > 1.
3. Rút gọn:
a) C= \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)....\left(1-\dfrac{1}{20}\right)\)
b) D= \(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2012}}\)
4. So sánh: E=\(\dfrac{20^{10}+1}{20^{10}-1}\) và F =\(\dfrac{20^{10}-1}{20^{10}-3}\)
5. Tính giá trị của biểu thức:
M= \(\dfrac{\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{3}{11}}{\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{11}}\)
Bai 5. Tinh nhanh
a, \(\dfrac{1}{5.8}+\dfrac{1}{8.7}+\dfrac{1}{11.14}+.......+\dfrac{1}{605.606}\)
b,\(\left(\dfrac{1}{10}-1\right)\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right)....\left(\dfrac{1}{2012}-1\right)\)
Tìm số nguyên \(x\), biết rằng :
\(4\dfrac{1}{3}.\left(\dfrac{1}{6}-\dfrac{1}{2}\right)\le x\le\dfrac{2}{3}.\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{4}\right)\)
tìm x biết :
a) \(\left|x+\dfrac{1}{2}\right|\)=\(\dfrac{5}{2}\) b) \(\left|2x-\dfrac{2}{3}\right|\)+\(\dfrac{1}{3}\)=0 c) |x-2| = 2x + 1
\(H=\dfrac{1}{7}.\left(-0,28\right)+\dfrac{2}{14}.16\%+\left(-3\dfrac{1}{7}\right).\dfrac{1}{25}\)
