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SP
1
DD
Đoàn Đức Hà
Giáo viên
22 tháng 4 2022
\(A=\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{8}+...+\dfrac{10}{2^{10}}\)
\(2A=\dfrac{1}{1}+\dfrac{2}{2}+\dfrac{3}{4}+...+\dfrac{10}{2^9}\)
\(2A-A=\left(1+\dfrac{2}{2}+\dfrac{3}{4}+...+\dfrac{10}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{2}{4}+...+\dfrac{10}{2^{10}}\right)\)
\(A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^9}-\dfrac{10}{2^{10}}\)
\(B=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^9}\)
\(2B=2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\)
\(2B-B=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^9}\right)\)
\(B=2-\dfrac{1}{2^9}\)
Suy ra \(A=B-\dfrac{10}{2^{10}}=2-\dfrac{1}{2^9}-\dfrac{10}{2^{10}}=\dfrac{509}{256}\)
HH
6
TD
2
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
26 tháng 12 2023
245 - 150 : [(23 - 13)2.(-4) -10] + 20233
= 245 - 150 : [(8 - 13)2..(-4) - 10] + 20233
= 245 - 150 : [(-5)2.(-4) - 10] + 20233
= 245 - 150 : [ -100 - 10] + 20233
= 245 - 150:(-110) + 20233
= 245 + \(\dfrac{15}{11}\) + 20233
= \(\dfrac{2710}{11}\) + 20233
NN
Mik cần gấp giúp mik ạ
2
11 tháng 12 2021
\(d,=\left(-1000\right).38.25\left(-2\right)=\left(-38000\right).\left(-50\right)=1900000\\ e,=29.\left(2021+2020-2021\right)+\left(120-49\right).2020\\ =29.2020+\left(120-49\right).2020=2020.\left(29+120-49\right)=2020.100=202000\\ f,=\left(-25\right)\left(2023-22-1\right)=\left(-25\right).2000=-50000\)
GH
Gia Hân
VIP
7 tháng 7 2023
a) \(\dfrac{-7}{5}\) . \(\dfrac{4}{23}\) + \(\dfrac{4}{23}\) . \(\dfrac{2}{5}\)
= \(\dfrac{4}{23}\) . ( \(\dfrac{-7}{5}\) + \(\dfrac{2}{5}\) )
= \(\dfrac{4}{23}\) . -1
= \(\dfrac{-4}{23}\)
GH
Gia Hân
VIP
7 tháng 7 2023
b) \(\dfrac{-6}{7}\) . \(\dfrac{3}{5}\) +\(\dfrac{-6}{7}\) .\(\dfrac{2}{5}\) - \(1\dfrac{1}{3}\)
= \(\dfrac{-6}{7}\) . \(\dfrac{3}{5}\) +\(\dfrac{-6}{7}\) .\(\dfrac{2}{5}\) - \(\dfrac{4}{3}\)
= \(\dfrac{-6}{7}\) . (\(\dfrac{3}{5}\) + \(\dfrac{2}{5}\) ) - \(\dfrac{4}{3}\)
= \(\dfrac{-6}{7}\) . 1 - \(\dfrac{4}{3}\)
= \(\dfrac{-6}{7}\) - \(\dfrac{4}{3}\)
= \(\dfrac{-18}{21}\) - \(\dfrac{28}{21}\)
= \(\dfrac{-18}{21}\) + \(\dfrac{-28}{21}\)
= \(\dfrac{-46}{21}\)
a: \(\dfrac{4}{13}+\dfrac{-12}{39}=\dfrac{4}{13}-\dfrac{4}{13}=0\)
b: \(\dfrac{27}{23}-\dfrac{-5}{21}-\dfrac{4}{23}+\dfrac{16}{21}+\dfrac{1}{2}\)
\(=\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)
\(=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)
c: \(\dfrac{-8}{9}+\dfrac{1}{9}\cdot\dfrac{2}{9}+\dfrac{1}{9}\cdot\dfrac{7}{9}\)
\(=\dfrac{-8}{9}+\dfrac{1}{9}\left(\dfrac{2}{9}+\dfrac{7}{9}\right)\)
\(=\dfrac{-8}{9}+\dfrac{1}{9}=\dfrac{-7}{9}\)
d: \(\dfrac{2}{\left(-3\right)^2}+\dfrac{5}{-12}-\dfrac{-3}{4}\)
\(=\dfrac{2}{9}-\dfrac{5}{12}+\dfrac{3}{4}\)
\(=\dfrac{8}{36}-\dfrac{15}{36}+\dfrac{27}{36}=\dfrac{19}{36}\)