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Ta có 1/2*3=1/2-1/3;
1/3*4=1/3-1/4
......................(tương tự với các số khác)
1/149*150=1/149-1/150
=>A=1/2-1/3+1/3-1/4+1/4-1/5+...-1/149+1/149-1/150=1/2-1/150
A=75/150-1/150=74/150=37/75
Vậy A= 37/75
Bài 1
A= 3.4 + 4.5+ 5.6+ .......+ 58.59 + 69.60
3A = 3.4.3 + 4.5.3+ 5.6.3+ .......+ 58.59.3 +59.60.3
= 3.4.(5-2) + 4.5.(6-3)+ 5.6.(7-4)+ .......+ 58.59.(60-57) +59.60.(61-58)
= 3.4.5-2.3.4+4.5.6-3.4.5+5.6.7-4.5.6+..........+ 58.59.60-57.58.59+ 59.60.61-58.59.60
=2.3.4+ 59.60.61= 215964
A= 215964: 3= 71988
Bài 2:
A = 2.4 +4.6+ 6.8+.........+ 96.98+98.100
6A= 2.4.6+4.6.6+6.8.6+.........+96.98.6+98.100.6
= 2.4.6+ 4.6.(8-2) +6.8.(10-4)+.........+96.98.( 100-94) + 98 .100.( 102 - 96)
= 2.4.6+4.6.8-2.4.6 + 6.8.10 -4.6.8+..........+ 96.98.100-94.96.98+ 98.100.102-96.98.100
= 98 .100 .102= 999600
A= 999600:6= 166600
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) \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+..........+\frac{1}{200.203}\)
\(=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+........+\frac{3}{200.203}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+......+\frac{1}{200}-\frac{1}{203}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{203}\right)=\frac{1}{3}.\frac{201}{406}=\frac{67}{406}\)
a) x+30%x=-1.31
=> 100%x+30%x=-1.31
=>x.(100%+30%)=-1.31
=>x.13/10=-1.31=-1.31:13/10=-131/130
b) (x-1/2):1/3+5/7=9+5/7
=>(x-1/2).3+5/7=68/7
=>(x-1/2).3=68/7-5/7=9
=>x-1/2=9:3=3
=>x=3+1/2=3 1/2( hỗn số)
c) 1/2x-3/4=14/9.3/7
=>1/2x-3/4=2/3
=>1/2x=2/3+3/4=17/12
x=17/12:1/2=17/12.2=17/6
d) - 5/6 -x = 7/12+ -1/3
=>- 5/6 -x = 7/12+ -4/12=1/4
=> x = -5/6 -1/4=-13/12
e) x + 3/-15 = 1/3
=> x= 1/3 - -3/15 =1/3+3/15
=> x=5/15 + 3/15=8/15
f) (4,5 -2 x). (-1 4/7)=11/14
=> 4,5 -2x=11/14 : -3/7=11/14. -7/3=-11/6
=>-2x=-11/6-9/2= -11/6 -27/6 =-19/3
=>x= -19/3: -2x=19/6
Chúc bn thi HKII tốt!!!
a) \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
=> \(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
=> \(A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)
a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66
= (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)
= 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)
= 25/66
b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7
= (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)
= 1/1 - 1/7 = 6/7
c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21
C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)
C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]
C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)
C = 1
Dễ nhưng dài quá !