Bài 7: Phép cộng phân số

\(=\dfrac{1}{11}+\dfrac{1}{11\cdot19}+\dfrac{1}{19\cdot27}+\dfrac{1}{27\cdot35}+\dfrac{1}{35\cdot43}+\dfrac{1}{43\cdot51}\)

\(=\dfrac{1}{11}+\dfrac{1}{8}\left(\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-...-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{11}+\dfrac{1}{8}\cdot\dfrac{40}{51\cdot11}\)

\(=\dfrac{1}{11}+\dfrac{5}{51\cdot11}=\dfrac{56}{51\cdot11}\)

\(\dfrac{1}{11}+\dfrac{1}{209}+\dfrac{1}{513}+\dfrac{1}{945}+\dfrac{1}{1505}+\dfrac{1}{2193}\)

\(=\dfrac{1}{11}+\dfrac{1}{11.19}+\dfrac{1}{19.27}+...+\dfrac{1}{43.51}\)

\(=\dfrac{1}{11}+\dfrac{1}{8}\left(\dfrac{8}{11.19}+\dfrac{8}{19.27}+...+\dfrac{8}{43.51}\right)\)

\(=\dfrac{1}{11}+\dfrac{1}{8}\left(\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{27}+...+\dfrac{1}{43}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{11}+\dfrac{1}{8}\left(\dfrac{1}{11}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{11}+\dfrac{5}{561}=\dfrac{56}{561}\)

`1+1/3-3/5+5/7-7/9+9/11-11/13-9/11+7/9-5/7 +3/5 - 1/3+1`

`=(1+1)+(1/3-1/3)+(-3/5+3/5)+(5/7-5/7)+(-7/9+7/9) +(9/11-9/11)-11/13`

`=2+0+0+0+0-11/13`

`=2-11/13`

`=26/13-11/13`

`=15/13`

\(=2+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{5}{7}+\dfrac{-7}{9}+\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{9}{11}-\dfrac{11}{13}\)

=2-11/13=15/13

19: =1+1+1/3-1/3-3/5+3/5+5/7-5/7-7/9+7/9+9/11-9/11-11/13

=2-11/13

=15/13

20: =1/11+1/11*19+1/19*27+...+1/43*51

=1/11+1/8(1/11-1/19+1/19-1/27+...+1/43-1/51)

=1/11+1/8*40/561

=1/11+5/561

=56/561

9: \(=\dfrac{1}{4}-\dfrac{1}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{98\cdot100}\right)\)

\(=\dfrac{1}{4}-\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\)

\(=\dfrac{1}{4}-\dfrac{1}{2}\cdot\dfrac{49}{100}=\dfrac{1}{4}-\dfrac{49}{200}=\dfrac{1}{200}\)

10: \(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{23\cdot27}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{27}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{8}{27}=\dfrac{1}{2}-\dfrac{2}{27}=\dfrac{23}{54}\)

7: \(=1-\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{63\cdot65}\right)\)

\(=1-\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{63}-\dfrac{1}{65}\right)\)

\(=1-\dfrac{62}{195}=\dfrac{133}{195}\)

8: \(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{19\cdot21}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{21}\right)=\dfrac{1}{2}\cdot\dfrac{20}{21}=\dfrac{10}{21}\)

`1/50 - 1/(50xx49)-1/(49xx48)-......-1/(2xx1)`

`=1/50 - (1/(1xx2)+1/(2xx3)+........+1/(49xx50))`

`=1/50 -(1-1/2+1/2-1/3+....+1/49-1/50)`

`=1/50-(1-1/50)`

`=1/50 - (50/50-1/50)`

`=1/50-49/50`

`=-48/50`

`=-24/25`

giúp mik nhé

\(=\dfrac{1}{50}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)

\(=\dfrac{1}{50}-1+\dfrac{1}{50}=\dfrac{1}{25}-1=-\dfrac{24}{25}\)

`-1/99 - 1/(99.98) - 1/(98.97) - 1/(97.96) - ... - 1/(3.2) - 1/(2.1)`

`= -1/99 - (1/(1.2) + 1/(2.3) + ... + 1/(98.99))`

`= -1/99 - (1/1 - 1/2 + 1/2 - 1/3 + ... + 1/98 - 1/99)`

`= -1/99 - (1/1 - 1/99)`

`= -1/99 - 98/99`

`= -1`

Các anh các chị giúp em bài này nhé

Chị Lê Michael có thấy thì giúp em nhé 

\(=\dfrac{-1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)

\(=\dfrac{-1}{99}-1+\dfrac{1}{99}=-1\)

\(=\dfrac{-1}{5}-\dfrac{13}{15}+\dfrac{5}{7}-\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{11}{13}\)

=-14/15

`(-1)/5 + 5/7 - 7/9+9/11-11/13-13/15+11/13-9/11+7/9-5/7`

`=-1/5+ 5/7 - 7/9+9/11-11/13-13/15+11/13-9/11+7/9-5/7`

`=(5/7-5/7)+(-7/9+7/9)+(9/11-9/11)+(-11/13+11/13)-1/5-13/15`

`=0+0+0+0-1/5-13/15`

`=-1/5-13/15`

`=-3/15-13/15`

`=-16/15`

\(=-\dfrac{14}{15}\)

`(-1)/3 + 3/4-4/5+5/6-6/7-7/8+6/7-5/6+4/5-3/4`

`=-1/3+ 3/4-4/5+5/6-6/7-7/8+6/7-5/6+4/5-3/4`

`=(3/4-3/4)+(-4/5+4/5)+(5/6-5/6)+(-6/7+6/7)-1/3 - 7/8`

`=0+0+0+0-1/3-7/8`

`=-1/3-7/8`

`=-8/24 - 21/24`

`=-29/24`

Ai giúp em với

\(A=\dfrac{1}{2}+\dfrac{5}{6}-\dfrac{1}{3}\)

\(\Rightarrow A=\dfrac{3}{6}+\dfrac{5}{6}-\dfrac{2}{6}\)

\(\Rightarrow A=\dfrac{3+5-2}{6}\)

\(\Rightarrow A=\dfrac{6}{6}=1\)