X +\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{97\times98}+\frac{1}{98\times99}\right)\)=10
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MT
1
28 tháng 8 2018
Ta có \(\frac{1}{2.3}-\frac{1}{3.4}=\frac{2}{2.3.4}\)...... , \(\frac{1}{97.98}-\frac{1}{98.99}=\frac{2}{97.98.99}\)
vậy 2 xA = \(\frac{2}{1.2.3.}\) -\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)-.\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\).....-\(\frac{1}{97.98}\)+\(\frac{1}{98.99}\)
=1/3-1/6+1/(98.99) =1/6 +1/(98.99)
=> A = 1/12+\(\frac{1}{2.98.99}\)
19 tháng 11 2017
Gọi \(A=\frac{1}{100.99}-\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(\Rightarrow A=\frac{1}{99.100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\right)\)
\(\Rightarrow A=\frac{1}{9900}-\left(1-\frac{1}{99}\right)\)
\(\Rightarrow A=\frac{1}{9900}-\frac{98}{99}=\frac{1}{9900}-\frac{9800}{9900}\)
\(\Rightarrow A=\frac{-9799}{9900}\)
TH
19 tháng 11 2017
\(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-....-\frac{1}{3.2}-\frac{1}{2.1}=-\left(\frac{1}{100.99}+\frac{1}{99.98}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)=-\left(1-\frac{1}{100}\right)=-\frac{99}{100}\)
19 tháng 11 2017
\(\dfrac{1}{100.99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
\(pt\Leftrightarrow\dfrac{1}{100.99}-\left(\dfrac{1}{99.98}+\dfrac{1}{98.97}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)
\(=\dfrac{1}{99.100}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{97.98}+\dfrac{1}{98.99}\right)\)
\(=\dfrac{1}{99.100}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{97}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{99.100}-\left(1-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{99}-\dfrac{1}{100}-1-\dfrac{1}{99}\)
\(=-\dfrac{1}{100}-1=-\dfrac{101}{100}\)
20 tháng 11 2017
\(\Rightarrow=\dfrac{1}{100.99}-\left(\dfrac{1}{99.98}+\dfrac{1}{99.97}+...+\dfrac{1}{2.1}\right)\)
\(\Rightarrow\dfrac{1}{100}-\left(\dfrac{1}{99}-\dfrac{1}{98}+\dfrac{1}{98}-....+\dfrac{1}{2}-1\right)\)
\(\Rightarrow\dfrac{1}{100}-\left(\dfrac{1}{99}-1\right)\)
\(\Rightarrow\dfrac{1}{100}-\dfrac{-98}{99}\)
=......... bn tính nhé