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2 tháng 7 2017

\(\dfrac{1.3.5+2.6.10+4.12.20+7.21.35}{1.5.7+2.10.14+4.20.28+7.35.49}\)

\(=\dfrac{1.3.5+2^3.1.3.5+2^6.1.3.5+7^3.1.3.5}{1.5.7+2^3.1.5.7+2^6.1.5.7+7^3.1.5.7}\)

\(=\dfrac{1.3.5\left(1+2^3+2^6+7^3\right)}{1.5.7\left(1+2^3+2^6+7^3\right)}\)

\(=\dfrac{1.3.5}{1.5.7}\)

2 tháng 7 2017

giúp mk vs các bn

26 tháng 4 2018

\(\dfrac{1\cdot3\cdot5+2\cdot6\cdot10+4\cdot12\cdot20+7\cdot21\cdot35}{1\cdot5\cdot7+2\cdot10\cdot14+4\cdot20\cdot28+7\cdot35\cdot45}\)

=\(\dfrac{3+6+12+21\cdot35}{14+28+7\cdot45}\)

=\(\dfrac{450}{119}\)

\(\dfrac{450}{119}>1\)\(1>\dfrac{303}{708}\)

\(\Rightarrow\)\(\dfrac{450}{119}>\dfrac{303}{708}\)

19 tháng 2 2017

\(\frac{2.6.10+6.10.14+10.14.18+...+194.198.202}{1.3.5+3.5.7+...+97.99.101}\)

\(=\frac{2^3.1.3.5+2^3.3.5.7+2^3.97.99.101}{1.3.5+3.5.7+...+97.99.101}\)

\(=\frac{2^3\left(1.3.5+3.5.7+...+97.99.101\right)}{1.3.5+3.5.7+...+97.99.101}\)

\(=\frac{2^3}{1}=8\)

Vậy A = 8

19 tháng 2 2017

Càm ơn bạn!

29 tháng 3 2017

\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}\)

\(=\frac{1.5.3.2+2.10.6.2+4.20.12.2+9.45.27.2}{1.3.5+2.6.10+4.12.20+9.27.45}\)

\(=\frac{2\left(1.3.5+2.6.10+4.12.20+9.27.45\right)}{1.3.5+2.6.10+4.12.20+9.27.45}\)

\(=2\)

23 tháng 7 2017

a, A= \(5\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\right)\)

\(A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(A=5\left(1-\dfrac{1}{100}\right)\)

\(A=5.\dfrac{99}{100}=\dfrac{99}{20}.\)

b, \(C=1.2.3+2.3.4+...+8.9.10\)

\(4C=1.2.3.4+2.3.4.\left(5-1\right)+...+8.9.10.\left(11-7\right)\)\(4C=1.2.3.4+2.3.4.5-1.2.3.4+...+8.9.10.11-7.8.9.10\)\(4C=8.9.10.11\)

\(C=\dfrac{8.9.10.11}{4}=1980.\)

c, https://hoc24.vn/hoi-dap/question/384591.html

Câu này bạn vào đây mình đã giải câu tương tự nhé.

23 tháng 7 2017

\(1)A=\dfrac{5}{1.2}+\dfrac{5}{2.3}+...+\dfrac{5}{99.100}\)

\(\Leftrightarrow A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(\Leftrightarrow A=5\left(1-\dfrac{1}{100}\right)\)

\(\Leftrightarrow A=5\cdot\dfrac{99}{100}\)

\(\Leftrightarrow A=\dfrac{99}{20}\)

10 tháng 7 2017

\(\dfrac{1\cdot2\cdot3+2\cdot4\cdot6+4\cdot8\cdot12}{1\cdot3\cdot5+2\cdot6\cdot10+4\cdot12\cdot20}\\ =\dfrac{1\cdot2\cdot3+2\cdot1\cdot2\cdot2\cdot2\cdot3+4\cdot1\cdot4\cdot2\cdot4\cdot3}{1\cdot3\cdot5+2\cdot1\cdot2\cdot3\cdot2\cdot5+4\cdot1\cdot4\cdot3\cdot4\cdot5}\\ =\dfrac{1\cdot2\cdot3\cdot\left(1+2^3+4^3\right)}{1\cdot3\cdot5\cdot\left(1+2^3+4^3\right)}\\ =\dfrac{1\cdot2\cdot3}{1\cdot3\cdot5}\\ =\dfrac{6}{15}\)

10 tháng 7 2017

cảm ơn bạn nhiều lắm haha

d)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.3+2.2.6+2.7.21}{3.5+3.2.10+3.7.35}=\frac{2.3+2.12+2.147}{3.5+3.20+3.245}=\frac{2\left(3+12+147\right)}{3\left(5+20+245\right)}\)

\(=\frac{2.162}{3.270}=\frac{54}{135}=\frac{2}{5}\)

3 tháng 5 2019

\(a.\frac{-2019.2018+1}{\left(-2017\right).\left(-2019\right)+2018}\)

\(=\frac{2019.\left(-2018\right)+1}{2019.2017+2018}\)

\(=\frac{2019.\left(-2018\right)+1}{2019.2018-1}\)

\(=-\frac{2018}{2018}\)

\(=-1\)

22 tháng 1 2016

\(C=\frac{1.5.3.2+2.10.6.2+4.20.12.2+...+9.45.27.2}{1.3.5+2.6.10+4.12.20+...+9.27.45}\)

 \(C=\frac{2\left(1.5.3+2.10.6+4.20.12+...+9.45.27\right)}{1.3.5+2.6.10+4.12.20+...+9.27.45}\) = 2

16 tháng 2 2022

1100444-88888=

a)\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{1}{2}.\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+\frac{11-9}{9.11}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{11}\right)\)

\(\frac{10}{22}\)

26 tháng 4 2017

a,\(\frac{4.7}{9.32}=\frac{7}{9.8}=\frac{7}{72}\)

26 tháng 4 2017

a) \(\frac{4.7}{9.32}\)=\(\frac{28}{288}\)=\(\frac{7}{72}\)

b)\(\frac{3.21}{14.15}\)=\(\frac{63}{210}\)=\(\frac{3}{10}\)

c)\(\frac{2.5.13}{26.35}\)=\(\frac{130}{910}\)=\(\frac{1}{7}\)

d)\(\frac{9.6-9.3}{18}\)=\(\frac{27}{18}\)=\(\frac{3}{2}\)

e)\(\frac{17.5-17}{3-20}\)=\(\frac{68}{-17}\)=\(-4\)

f)\(\frac{49+7.49}{49}\)=\(\frac{392}{49}\)=\(8\)