1/2 +1/14 +1/21 +....+1/4850
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Đặt tổng A ta có :
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{35}+...+\frac{1}{4850}\)
\(\frac{3}{2}A=\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{1}{130}+...+\frac{3}{9700}\)
\(\frac{3}{2}A=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\)
\(\frac{3}{2}A=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow A=\frac{33}{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+...+\frac{1}{4850}\)
\(=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+...+\frac{2}{9700}\)
\(=2.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{97.100}\right)\)
\(=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{97.100}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{100}\right)\)
\(=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)
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a: =1/8-1/8+2/5=2/5
b: =(-1/15-14/15)+(23/27+31/27)=2-1=1
c: \(=\dfrac{3}{7}\left(\dfrac{22}{21}+\dfrac{5}{21}+\dfrac{15}{21}\right)=\dfrac{3}{7}\cdot2=\dfrac{6}{7}\)
d: \(=\dfrac{-8}{9}\cdot\dfrac{3}{2}+\dfrac{1}{9}\cdot\dfrac{-3}{2}=-\dfrac{3}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
( \(\dfrac{1}{2}\) - \(\dfrac{13}{14}\)): \(\dfrac{5}{7}\) - (- \(\dfrac{2}{21}\) + \(\dfrac{1}{7}\)) : \(\dfrac{5}{7}\)
(\(\dfrac{7}{14}\) - \(\dfrac{13}{14}\)): \(\dfrac{5}{7}\) - ( - \(\dfrac{2}{21}\) + \(\dfrac{3}{21}\)): \(\dfrac{5}{7}\)
- \(\dfrac{6}{14}\): \(\dfrac{5}{7}\) - \(\dfrac{1}{21}\): \(\dfrac{5}{7}\)
= - (\(\dfrac{3}{7}\) + \(\dfrac{1}{21}\)): \(\dfrac{5}{7}\)
= -\(\dfrac{10}{21}\): \(\dfrac{5}{7}\)
= - \(\dfrac{2}{3}\)
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1.-14*63+(-14)*37=-14*(63+37)=-14*100=-1400
2.-21*21+21*(-79)=21*[-21+(-79)]=21*(-100)=-2100
cho mình nha!Thank you!