Ta có :3²/8*11+3²/11*14+3²/14*17+...............+3²/197*200

=3*(3/8*11+3/11*14+3/14*17+..............+3/197*200)

=3*(1/8-1/11+1/11-1/14+1/14-1/17+..................+1/197-1/200)

=3*(1/8-1/200) 

=3* (3/25)

=9/25

\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\)

\(=\)\(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{10}{20}-\frac{1}{20}\)

\(=\frac{9}{20}\)

Tk giúp !!

a ) 10 + 12 + 14 + 16 + 18 + 20 

= ( 10 + 20 ) + ( 14 + 16 ) + ( 12 + 18 )
=  30 + 30 + 30 

=  90

b ) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

= ( 19 + 1 ) + ( 17 + 3 ) + ( 15 + 5 ) + ( 7 + 13 ) + ( 9 + 11 )

= 20 + 20 + 20 + 20 + 20

= 100

c ) 75 + 110 + 25 + 90 + 200

= ( 75 + 25 ) + ( 110 + 90 ) + 200

= 100 + 200 + 200

= 500

do em chưa học tính chất dãy số nên không còn cách nhanh hơn 

a 10 + 12 + 14 + 16 + 18 + 20

= ( 10 + 20 ) + ( 14 + 16 ) + ( 12 + 18 )

= 40 + 40 + 40

= 40 x 3

= 120

b 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

= ( 1 + 19 ) + ( 3 + 17 ) + ( 5 + 15 ) + ( 7 + 13 ) + ( 9 + 11 )

= 20 + 20 + 20 + 20 + 20

= 20 x 5

= 100

c 75 + 110 + 25 + 90 + 200

= ( 75 + 25 ) + ( 110 + 90 ) + 200

= 100 + 200 + 200

= 500

10+12+14+16+18+20=90

1+3+5+7+9+11+13+15+17+19=100

75+110+25+90+200=500

tk nhé

\(E=\frac{3^2}{8.11}+\frac{3^2}{11.14}+\frac{3^2}{14.17}+...+\frac{3^2}{197.200}\)

\(=\frac{9}{8.11}+\frac{9}{11.14}+\frac{9}{14.17}+...+\frac{9}{197.200}\)

\(\Rightarrow\frac{1}{3}.E=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)

\(=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\)

\(=\frac{1}{8}-\frac{1}{200}=\frac{3}{25}\)

\(\Rightarrow E=\frac{3}{25}\div\frac{1}{3}=\frac{9}{25}\)

khó thế toy ko bt =)))

toy cũng vậy

1) \(\left(+15\right)+\left(+17\right)=15+17=32\)

2) \(\left(-3\right)+\left(-7\right)=-3-7=-\left(3+7\right)=-10\)

3) \(\left(-25\right)+\left(+4\right)=-25+4=-\left(25-4\right)=-21\)

4) \(\left(-6\right)+\left(-54\right)=-6-54=-\left(6+54\right)=-60\)

5) \(\left(-15\right)+20=20-15=5\)

6) \(\left(-5\right)+8+7+5\)

\(=\left(-5+5\right)+\left(8+7\right)\)

\(=15\)

7) \(\left(-8\right)+\left(-11\right)+\left(-2\right)\)

\(=\left[\left(-8\right)+\left(-2\right)\right]+\left(-11\right)\)

\(=\left(-10\right)+\left(-11\right)\)

\(=-21\)

8) \(15+\left(-5\right)+\left(-14\right)+\left(-16\right)\)

\(=\left[15+\left(-5\right)\right]+\left[\left(-14\right)+\left(-16\right)\right]\)

\(=10+\left(-30\right)\)

\(=-20\)

9) \(\left(-20\right)+\left(-14\right)+3+\left(-86\right)\)

\(=\left[\left(-20\right)+3\right]+\left[\left(-14\right)+\left(-86\right)\right]\)

\(=\left(-17\right)+\left(-100\right)\)

\(=-117\)

10) \(\left(-136\right)+123+\left(-264\right)+\left(-83\right)+240\)

\(=\left[\left(-136\right)+\left(-264\right)\right]+\left[123+\left(-83\right)\right]+240\)

\(=\left(-400\right)+40+240\)

\(=\left(-360\right)+240\)

\(=-120\)

11) \(\left(-596\right)+2001+1999+\left(-404+189\right)\)

\(=\left(-596\right)+2001+1999-404+189\)

\(=\left[\left(-596\right)-404\right]+\left(2001+189\right)+1999\)

\(=\left(-1000\right)+2190+1999\)

\(=1190+1999\)

\(=3189\)

12) \(314+\left(-153\right)+64+121+\left(-247\right)+218\)

\(=\left(314+64+121\right)+\left[\left(-153\right)+\left(-247\right)\right]+218\)

\(=\left(378+121\right)+\left(-400\right)+218\)

\(=499-400+218\)

\(=99+218\)

\(=317\)

\(\text{#}Toru\)

a) \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+........+\frac{1}{99.100}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.........+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

b) \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+..........+\frac{2}{73.75}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{73}-\frac{1}{75}\)

\(=\frac{1}{3}-\frac{1}{75}=\frac{8}{25}\)

c) \(\frac{4}{4.6}+\frac{4}{6.8}+\frac{4}{8.10}+..........+\frac{4}{64.66}\)

\(=2.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+..........+\frac{2}{64.66}\right)\)

\(=2.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+.....+\frac{1}{64}-\frac{1}{66}\right)\)

\(=2.\left(\frac{1}{4}-\frac{1}{66}\right)=2.\frac{31}{132}=\frac{31}{66}\)

d) \(\frac{9}{5.8}+\frac{9}{8.11}+\frac{9}{11.14}+........+\frac{9}{497.500}\)

\(=3.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+..........+\frac{3}{497.500}\right)\)

\(=3.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+......+\frac{1}{497}-\frac{1}{500}\right)\)

\(=3.\left(\frac{1}{5}-\frac{1}{500}\right)=3.\frac{99}{500}=\frac{297}{500}\)

e) \(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+......+\frac{1}{93.95}\)

\(=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+........+\frac{2}{93.95}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+........+\frac{1}{93}-\frac{1}{95}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{95}\right)=\frac{1}{2}.\frac{18}{95}=\frac{9}{95}\)

g) \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+..........+\frac{1}{200.203}\)

\(=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+........+\frac{3}{200.203}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+......+\frac{1}{200}-\frac{1}{203}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{203}\right)=\frac{1}{3}.\frac{201}{406}=\frac{67}{406}\)

bạn juventus ơi , bạn làm nốt cho mình mấy câu sau với 

= 1+(2-3)+(4-5)+(6-7)+........+(18-19)+20

= 1+(-1)+(-1)+(-1)+........+(-1)+20

= 1+(-9)+20

= 12

Tính: 1+2-3+4-5+6-7+8-9+10-11+12-13+14-15+16-17+18-19+20 = ?

= 1+(2-3)+(4-5)+(6-7)+........+(18-19)+20

= 1+(-1)+(-1)+(-1)+........+(-1)+20

= 1+(-9)+20

= 12

nhé !

Giải như trên thì kết quả đúng, nhưng cách giải thì lớp 3 chưa được giải số âm ạ!