E=\(\dfrac{0,5}{1x2}\)+\(\dfrac{0,5}{2x3}\)+\(\dfrac{0,5}{3x4}\)+......+\(\dfrac{0,5}{198x199}\)+\(\dfrac{0,5}{199x200}\)
K
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Những câu hỏi liên quan
TM
17 tháng 11 2017
Ta có:
\(A=\dfrac{0,5}{3}+\dfrac{0,5}{6}+\dfrac{0,5}{10}+...+\dfrac{0,5}{1275}+\dfrac{0,5}{1326}\)
\(\Rightarrow A=0,5\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+....+\dfrac{1}{1275}+\dfrac{1}{1326}\right)\)
\(\Rightarrow A=0,5.2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{10}+....+\dfrac{1}{2550}+\dfrac{1}{2652}\right)\)
\(\Rightarrow A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{10}+....+\dfrac{1}{2550}+\dfrac{1}{2652}\)
\(\Rightarrow A=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+....+\dfrac{1}{50.51}+\dfrac{1}{51.52}\)
\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{50}-\dfrac{1}{51}+\dfrac{1}{51}-\dfrac{1}{52}\)\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{52}=\dfrac{26}{52}-\dfrac{1}{52}=\dfrac{25}{52}\)
NT
2
6 tháng 10 2021
\(D=\dfrac{5}{1\cdot2}+...+\dfrac{5}{199\cdot200}\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{199}{200}=\dfrac{199}{80}\)
AH
Akai Haruma
Giáo viên
6 tháng 10 2021
Lời giải:
\(D=5\times \left(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{199\times 200}\right)\)
\(=5\times \left(\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+...+\frac{200-199}{199\times 200}\right)\)
\(=5\times \left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}\right)=5\times (1-\frac{1}{200})\)
\(=5\times \frac{199}{200}=\frac{995}{200}=\frac{199}{40}\)
22 tháng 12 2021
\(\Leftrightarrow\left(x-0.5\right)\cdot\dfrac{-4}{x-0.5}=-1\cdot\left(-4\right)\)
=>-4=4(loại)
TT
18 tháng 4 2021
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
18 tháng 4 2021
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
Y
22 tháng 6 2023
\(e,\sqrt{\dfrac{9}{169}}=\dfrac{\sqrt{9}}{\sqrt{169}}=\dfrac{\sqrt{3^2}}{\sqrt{13^2}}=\dfrac{3}{13}\)
\(f,\sqrt{1\dfrac{9}{16}}=\sqrt{\dfrac{25}{16}}=\dfrac{\sqrt{25}}{\sqrt{16}}=\dfrac{\sqrt{5^2}}{\sqrt{4^2}}=\dfrac{5}{4}\)
\(g,\dfrac{\sqrt{2300}}{\sqrt{23}}=\sqrt{\dfrac{2300}{23}}=\sqrt{100}=\sqrt{10^2}=10\)
\(h,\dfrac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\dfrac{12,5}{0,5}}=\sqrt{25}=\sqrt{5^2}=5\)
H9
HT.Phong (9A5)
CTVHS
22 tháng 6 2023
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, \(\dfrac{\sqrt{12,5}}{\sqrt{0,5}}\)
\(=\dfrac{\dfrac{5\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}\)
\(=\dfrac{\dfrac{5\sqrt{2}}{2}\cdot2}{\sqrt{2}}\)
\(=\dfrac{5\sqrt{2}}{\sqrt{2}}=5\)
E=0,5 x 199/200=199/400
\(E=\dfrac{0.5}{1.2}+\dfrac{0.5}{2\cdot3}+...+\dfrac{0.5}{199\cdot200}\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{200}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{199}{200}=\dfrac{199}{400}\)