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1x2+3x1+4x2+5x1+6
= 2 + 3 + 8 + 5 + 6
= 5 + 8 + 5 + 6
= 13 + 5 + 6
= 24

b) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}\)
\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)
\(=\frac{1}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{2015-2013}{2013.2015}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{2015}\right)=\frac{1007}{2015}\)
Phương trình tương đương với:
\(\frac{1007X}{2015}=\frac{4}{2015}\Leftrightarrow X=\frac{4}{1007}\)
c) \(\frac{x+1}{2015}+\frac{x+2}{2016}=\frac{x+3}{2017}+\frac{x+4}{2018}\)
\(\Leftrightarrow\frac{x+1}{2015}-1+\frac{x+2}{2016}-1=\frac{x+3}{2017}-1+\frac{x+4}{2018}-1\)
\(\Leftrightarrow\frac{x-2014}{2015}+\frac{x-2014}{2016}=\frac{x-2014}{2017}+\frac{x-2014}{2018}\)
\(\Leftrightarrow x-2014=0\)
\(\Leftrightarrow x=2014\)


a, Đặt :
\(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+..............+\dfrac{1}{19.21}\)
\(\Leftrightarrow2A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+............+\dfrac{2}{19.21}\)
\(\Leftrightarrow2A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+..........+\dfrac{1}{19}-\dfrac{1}{21}\)
\(\Leftrightarrow2A=1-\dfrac{1}{21}\)
\(\Leftrightarrow2A=\dfrac{20}{21}\)
\(\Leftrightarrow A=\dfrac{10}{21}\)
b, \(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+...........+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\)
\(\Leftrightarrow2A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+............+\dfrac{2}{\left(2n-1\right)\left(2n+1\right)}\)
\(\Leftrightarrow2A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+........+\dfrac{1}{2n-1}-\dfrac{1}{2n+1}\)
\(\Leftrightarrow2A=1-\dfrac{1}{2n+1}\)
\(\Leftrightarrow2A=\dfrac{2n}{2n+1}\)
\(\Leftrightarrow A=\dfrac{n}{2n+1}\)




Đặt \(A=\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-....-\frac{1}{5.3}-\frac{1}{3.1}\)
\(\Rightarrow A=\frac{1}{99.97}-\left(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{93.95}+\frac{1}{95.97}\right)\)
\(\Rightarrow A=\frac{1}{99.97}-\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{95}-\frac{1}{97}\right)\)
\(\Rightarrow A=\frac{1}{99}-\frac{1}{97}-\frac{1}{2}\left(1-\frac{1}{97}\right)=\frac{1}{99}-\frac{1}{97}-\frac{1}{2}-\frac{1}{194}\)

Đặt \(A=\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(-A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\)
\(-A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\)
\(-A=1-\frac{1}{99}\)
\(-A=\frac{98}{99}\)
\(A=\frac{-98}{99}\)
Chúc bạn học tốt ~
Đặt A = \(\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
=> - A = \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\)
- A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\)
- A = \(1-\frac{1}{99}\)
- A = \(\frac{98}{99}\)
=> A = \(-\frac{98}{99}\)
Vậy A = \(-\frac{98}{99}\)
Hok tốt
Trả lời :
= 12
HokT~
:)
1 + 1 x 2 + 1 x 1 + 2 x 1 + 1 x 3 + 3 x 1 = 12
~Chúc anh hok tốt~
#Sa-ngu-ngốc