Tính giá trị biểu thức:
B=\(\dfrac{5}{1\times2}+\dfrac{13}{2\times3}+\dfrac{25}{3\times4}+\dfrac{41}{4\times5}+...+\dfrac{181}{9\times10}\)
Những câu hỏi liên quan
tính tổng :\(B=\frac{5}{1\times2}+\frac{13}{2\times3}+\frac{25}{3\times4}+\frac{41}{4\times5}+...+\frac{181}{9\times10}\)
B=2+1/1.2+2+1/2.3+........+2+1/9.10
B=2.9+1/1.2+1/2.3+........+1/9.10
B=18+9/10
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Tính giá trị của mỗi phân số sau:
\(E=\dfrac{11\times3^{29}-\left(3^2\right)^{15}}{2\times3^{14}\times2\times3^{14}}\)
\(G=\dfrac{5\times3^{11}+4\times3^{12}}{3^9\times5^2-3^0\times2^3}\)
\(H=\dfrac{\left(3\times4\times2^{16}\right)^2}{11\times2^{13}\times4^{11}-16^9}\)
\(E=\dfrac{11.3^{29}-3^{2^{15}}}{2.3^{14}.2.3^{14}}\)
\(=\dfrac{11.3-3^{30}}{2^2}=\dfrac{33-3^{30}}{4}\)
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\(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{48\times49\times50}\)
\(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{48\times49\times50}\)
\(=\dfrac{1}{1\times2}-\dfrac{1}{2\times3}+\dfrac{1}{2\times3}-\dfrac{1}{3\times4}+\dfrac{1}{3\times4}-\dfrac{1}{4\times5}+...+\dfrac{1}{48\times49}-\dfrac{1}{49\times50}\)
\(=\dfrac{1}{1\times2}-\dfrac{1}{49\times50}\)
\(=\dfrac{1}{2}-\dfrac{1}{2450}\)
\(=\dfrac{612}{1225}\)
\(\text{#}Toru\)
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23 tháng 7 2023 lúc 14:17
\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+...+\dfrac{1}{98\times99}+\dfrac{1}{99\times100}\)
\(\dfrac{2}{11\times13}+\dfrac{2}{13\times15}+...+\dfrac{2}{19\times21}+\dfrac{2}{21\times23}\)
\(1,\\ =\dfrac{2-1}{1\times2}+\dfrac{3-2}{2\times3}+\dfrac{4-3}{3\times4}+\dfrac{5-4}{4\times5}+.....+\dfrac{99-98}{98\times99}+\dfrac{100-99}{99\times100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+....+\dfrac{1}{98}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}=\dfrac{100-1}{100}=\dfrac{99}{100}\)
\(2,=\dfrac{13-11}{11\times13}+\dfrac{15-13}{13\times15}+....+\dfrac{21-19}{19\times21}+\dfrac{23-21}{21\times23}\\ =\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+....+\dfrac{1}{19}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{23}\\ =\dfrac{1}{11}-\dfrac{1}{23}\\ =\dfrac{23-11}{11\times23}=\dfrac{12}{253}\)
@seven
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a: 1/1*2+1/2*3+...+1/99*100
=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=99/100
b: 2/11*13+2/13*15+...+2/21*23
=1/11-1/13+1/13-1/15+...+1/21-1/23
=1/11-1/23
=12/253
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\(\dfrac{4^{10}\times9^6+3^{12}\times8^5}{6^{13}\times4-2^{16}\times3^{12}}\)
\(\dfrac{2^4\times2^6}{\left(2^5\right)^2}-\dfrac{2^5\times15^3}{6^3\times10^2}\)
\(\dfrac{\left(-2\right)^{10}\times3^{31}+2^{40}\times\left(-3\right)^6}{\left(-2\right)^{11}\times\left(-3\right)^{31}+2^{41}\times3^6}\)
giải chi tiết giúp mình nhé
chứng minh
M=\(\dfrac{3}{1^2\times2^2}+\dfrac{5}{2^2\times3^2}+\dfrac{7}{3^2\times4^2}+.......+\dfrac{19}{9^2\times10^2}< 1\)
\(M=\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{19}{9^2.10^2}\)
\(M=\dfrac{2^2-1^2}{1^2.2^2}+\dfrac{3^2-2^2}{2^2.3^2}+\dfrac{4^2-3^2}{3^2.4^2}+...+\dfrac{10^2-9^2}{9^2.10^2}\)
\(M=1-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{9^2}-\dfrac{1}{10^2}\)
\(M=1-\dfrac{1}{10^2}< 1\left(đpcm\right)\)
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21 tháng 2 2023 lúc 19:00
Bài 2: Tính
a) \(\dfrac{30\times25\times7\times8}{75\times8\times12\times14}\)
b)\(\dfrac{8\times3\times4}{16\times3}\)
c)\(\dfrac{4\times5\times6}{3\times10\times8}\)
(Các bạn tách các số ra rồi gạch, gạch xong thì nhân lại và ra kết quả) Thanks
a) \(\dfrac{30\times25\times7\times8}{75\times8\times12\times14}=\dfrac{3\times2\times5\times25\times7\times8}{25\times3\times8\times3\times4\times2\times7}=\dfrac{5}{3\times4}=\dfrac{5}{12}\)
b) \(\dfrac{8\times3\times4}{16\times3}=\dfrac{8\times3\times2\times2}{8\times2\times3}=2\)
c) \(\dfrac{4\times5\times6}{3\times10\times8}=\dfrac{4\times5\times3\times2}{3\times5\times2\times4\times2}=\dfrac{1}{2}\)
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giúp mik với ạ, mình sẽ tick ạ! Thanks.
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Tính bằng cách hợp lí :
a , dfrac{1}{15}+dfrac{9}{10}+dfrac{14}{15}-dfrac{11}{9}-dfrac{20}{10}+dfrac{1}{157}
b , dfrac{1}{5}-dfrac{-1}{3}+dfrac{-1}{5}-dfrac{2}{6}
c , dfrac{2}{1times3}+dfrac{2}{3times5}+...+dfrac{2}{2015times2017}
d , dfrac{5}{1times3}+dfrac{5}{3times5}+...+dfrac{5}{2015times2017}
e , dfrac{1}{1times2}+dfrac{1}{3times4}+...+dfrac{1}{2016times2017}
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Tính bằng cách hợp lí :
a , \(\dfrac{1}{15}+\dfrac{9}{10}+\dfrac{14}{15}-\dfrac{11}{9}-\dfrac{20}{10}+\dfrac{1}{157}\)
b , \(\dfrac{1}{5}-\dfrac{-1}{3}+\dfrac{-1}{5}-\dfrac{2}{6}\)
c , \(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+...+\dfrac{2}{2015\times2017}\)
d , \(\dfrac{5}{1\times3}+\dfrac{5}{3\times5}+...+\dfrac{5}{2015\times2017}\)
e , \(\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+...+\dfrac{1}{2016\times2017}\)
a: \(=\left(\dfrac{1}{15}+\dfrac{14}{15}\right)+\left(\dfrac{9}{10}-2-\dfrac{11}{9}\right)+\dfrac{1}{157}\)
\(=1+\dfrac{1}{157}+\dfrac{81-180-110}{90}\)
\(=\dfrac{158}{157}+\dfrac{-209}{90}\simeq-1.315\)
b: \(=\dfrac{1}{5}+\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{2}{6}\)
=1/3-1/3
=0
c: \(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2015\cdot2017}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2015}-\dfrac{1}{2017}\)
=2016/2017
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a)\(\left(\dfrac{17}{10}+7-8,7\right)\div\left(\dfrac{23}{4}-\dfrac{11}{4}+\dfrac{9}{25}\right)\times\left(12,98\times0,25\right)+12,5\)
b)\(1\dfrac{2}{24}\times5\dfrac{2}{5}\times2\times3\dfrac{7}{9}\times2\times\dfrac{2}{17}\)
a: \(=\left(\dfrac{17}{10}+\dfrac{70}{10}-\dfrac{87}{10}\right):\left(\dfrac{23}{4}-\dfrac{11}{4}+\dfrac{9}{25}\right)\cdot\left(12,98\cdot0,25\right)+12,5\)
\(=0:\left(3+\dfrac{9}{25}\right)\cdot\left(12,98+0,25\right)+12,5\)
=12,5
b: \(=\dfrac{13}{12}\cdot\dfrac{27}{5}\cdot2\cdot\dfrac{34}{9}\cdot2\cdot\dfrac{2}{17}\)
\(=\dfrac{13}{12}\cdot2\cdot\dfrac{27}{5}\cdot\dfrac{34}{9}\cdot\dfrac{4}{17}\)
\(=\dfrac{13}{6}\cdot\dfrac{27}{5}\cdot\dfrac{8}{9}=\dfrac{8}{6}\cdot3\cdot\dfrac{13}{5}=4\cdot\dfrac{13}{5}=\dfrac{52}{5}\)
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