E=\(\dfrac{0,5}{1x2}\)+\(\dfrac{0,5}{2x3}\)+\(\dfrac{0,5}{3x4}\)+......+\(\dfrac{0,5}{198x199}\)+\(\dfrac{0,5}{199x200}\)
B= \(\dfrac{1}{1x2}\)+\(\dfrac{1}{2x3}\)+\(\dfrac{1}{3x4}\)+.....+\(\dfrac{1}{198x199}\)+\(\dfrac{1}{199x200}\)
\(B=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{199\times200}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\)
\(=1-\dfrac{1}{200}=\dfrac{199}{200}\)
Tính A=\(\dfrac{0,5}{3}+\dfrac{0,5}{6}+\dfrac{0,5}{10}+\dfrac{0,5}{15}+...+\dfrac{0,5}{1275}+\dfrac{0,5}{1326}\)
Ta có:
\(A=\dfrac{0,5}{3}+\dfrac{0,5}{6}+\dfrac{0,5}{10}+...+\dfrac{0,5}{1275}+\dfrac{0,5}{1326}\)
\(\Rightarrow A=0,5\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+....+\dfrac{1}{1275}+\dfrac{1}{1326}\right)\)
\(\Rightarrow A=0,5.2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{10}+....+\dfrac{1}{2550}+\dfrac{1}{2652}\right)\)
\(\Rightarrow A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{10}+....+\dfrac{1}{2550}+\dfrac{1}{2652}\)
\(\Rightarrow A=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+....+\dfrac{1}{50.51}+\dfrac{1}{51.52}\)
\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{50}-\dfrac{1}{51}+\dfrac{1}{51}-\dfrac{1}{52}\)\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{52}=\dfrac{26}{52}-\dfrac{1}{52}=\dfrac{25}{52}\)
D=\(\dfrac{5}{1x2}\)+\(\dfrac{5}{2x3}\)+\(\dfrac{5}{3x4}\)+....+\(\dfrac{5}{199x200}\)
\(D=\dfrac{5}{1\cdot2}+...+\dfrac{5}{199\cdot200}\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{199}{200}=\dfrac{199}{80}\)
Lời giải:
\(D=5\times \left(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{199\times 200}\right)\)
\(=5\times \left(\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+...+\frac{200-199}{199\times 200}\right)\)
\(=5\times \left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}\right)=5\times (1-\frac{1}{200})\)
\(=5\times \frac{199}{200}=\frac{995}{200}=\frac{199}{40}\)
\(\dfrac{-1}{\dfrac{4}{0,5-x}}=\dfrac{x-0,5}{4}\)
\(\Leftrightarrow\left(x-0.5\right)\cdot\dfrac{-4}{x-0.5}=-1\cdot\left(-4\right)\)
=>-4=4(loại)
\(\dfrac{5}{9}\):\(\dfrac{13}{7}\)+\(\dfrac{5}{9}\):\(\dfrac{13}{9}\)-1\(\dfrac{2}{3}\)
4\(\dfrac{2}{5}\):0,5%-1\(\dfrac{3}{7}\).14%+(-0,5)
Tính giúp mik với!!! Mình cảm ơn
a) \(\dfrac{5}{9}:\left(\dfrac{13}{7}+\dfrac{13}{9}\right)-\dfrac{5}{3}\)(chỗ này mk lười chép lại đề)
=\(\dfrac{5}{9}:\dfrac{208}{63}-\dfrac{5}{3}\)
=\(\dfrac{5}{9}.\dfrac{63}{208}-\dfrac{5}{3}\)
=\(\dfrac{5.63}{9.208}-\dfrac{5}{3}\)
=\(\dfrac{5.7}{1.208}-\dfrac{5}{3}\)
=\(\dfrac{36}{208}-\dfrac{5}{3}\)
=\(\dfrac{108}{624}-\dfrac{1040}{624}\)
=\(\dfrac{-932}{624}\)
=\(\dfrac{233}{156}\)
còn câu b mk chưa học nên mk chịu
Giải:
5/9:13/7+5/9:13/9 -1 2/3
=5/9.7/13+5/9.9/13-5/3
=5/9.(7/13+9/13)-5/3
=5/9.16/13-5/3
=80/117-5/3
=-115/117
4 2/5 : 0,5% -1 3/7 .14% +(-0,5)
=22/5:1/200-10/7.7/50 +(-1/2)
=880-1/5-1/2
=8793/10
A= ( -6,17 + \(3\dfrac{5}{9}\) - \(2\dfrac{36}{97}\)) . (\(\dfrac{1}{3}\) - 0,25 - \(\dfrac{1}{12}\))
B= \(\dfrac{0,5-\dfrac{3}{17}}{\dfrac{5}{6}-\dfrac{5}{17}}\) + \(\dfrac{0,5-\dfrac{1}{3}-0,2}{\dfrac{7}{5}+\dfrac{7}{3}-3,5}\)
A = \(\left(-6,17+3\dfrac{5}{9}-2\dfrac{36}{97}\right)\) . \(\left(\dfrac{1}{3}-0,25-\dfrac{1}{12}\right)\)
A = \(\left(-6,17+\dfrac{32}{9}-\dfrac{230}{97}\right)\) . \(\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\)
A = \(\left(-6,17+\dfrac{32}{9}-\dfrac{230}{97}\right)\) . \(\left(\dfrac{4}{12}-\dfrac{3}{12}-\dfrac{1}{12}\right)\)
A = \(\left(-6,17+\dfrac{32}{9}-\dfrac{230}{97}\right)\) . 0
A = 0*
*Vì số nào nhân với 0 cũng bằng 0 nên không cần tính kết quả của phép tính\(\left(-6,17+\dfrac{32}{9}-\dfrac{230}{97}\right)\)
tính:
a) \(25\%-\dfrac{5}{4}+1\dfrac{5}{6}\)
b) \(75\%:2\dfrac{1}{5}-\left(0,5\right)^2.\left(-7\right)+2,5\left(7\dfrac{2}{3}-5\dfrac{2}{3}\right)\)
c) \(45:2\dfrac{4}{7}+50\%-1,25\)
d) \(350\%:\dfrac{105}{24}+4\dfrac{5}{6}:2-\left(0,5\right)^2.30\%\)
e) \(4\dfrac{2}{5}.0,5-1\dfrac{3}{7}.14\%+\left(-0,8\right)\)
e,\(\sqrt{\dfrac{9}{169}}\)
f,\(\sqrt{1\dfrac{9}{16}}\)
g,\(\dfrac{\sqrt{2300}}{\sqrt{23}}\)
h,\(\dfrac{\sqrt{12,5}}{\sqrt{0,5}}\)
\(e,\sqrt{\dfrac{9}{169}}=\dfrac{\sqrt{9}}{\sqrt{169}}=\dfrac{\sqrt{3^2}}{\sqrt{13^2}}=\dfrac{3}{13}\)
\(f,\sqrt{1\dfrac{9}{16}}=\sqrt{\dfrac{25}{16}}=\dfrac{\sqrt{25}}{\sqrt{16}}=\dfrac{\sqrt{5^2}}{\sqrt{4^2}}=\dfrac{5}{4}\)
\(g,\dfrac{\sqrt{2300}}{\sqrt{23}}=\sqrt{\dfrac{2300}{23}}=\sqrt{100}=\sqrt{10^2}=10\)
\(h,\dfrac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\dfrac{12,5}{0,5}}=\sqrt{25}=\sqrt{5^2}=5\)
e, \(\sqrt{\dfrac{9}{169}}\)
\(=\sqrt{\dfrac{3^2}{13^2}}\)
\(=\dfrac{3}{13}\)
f, \(\sqrt{1\dfrac{9}{16}}\)
\(=\sqrt{\dfrac{25}{16}}\)
\(=\sqrt{\dfrac{5^2}{4^2}}\)
\(=\dfrac{5}{4}\)
g, \(\dfrac{\sqrt{2300}}{\sqrt{23}}\)
\(=\dfrac{10\sqrt{23}}{\sqrt{23}}\)
\(=10\)
h, \(\dfrac{\sqrt{12,5}}{\sqrt{0,5}}\)
\(=\dfrac{\dfrac{5\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}\)
\(=\dfrac{\dfrac{5\sqrt{2}}{2}\cdot2}{\sqrt{2}}\)
\(=\dfrac{5\sqrt{2}}{\sqrt{2}}=5\)
1: trong các trường hợp sau, trường hợp nào các số cùng biểu thị một số hữu tỉ:
A) 0,5; \(\dfrac{5}{10}\); \(\dfrac{1}{2}\) B) o,4; 2; \(\dfrac{1}{2}\) C) 0,5; 0,25, 0,35 D) \(\dfrac{-5}{7}\) ; \(\dfrac{-5}{8}\); \(\dfrac{-5}{9}\)