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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
5/-6 + -5/12 + 7/18
= -30/36 + -15/36 + 14/36
= ( -30 + -15 + 14 ) /36
= -31/36
-1 +2 - 3 + 4 - 5 + 6 + ........ + 2010 - 2011
= -1 + -1 + -1 + -1 + ......... + - 1
= [ ( - 1 ) - ( -1 ) ] + 1
= 0+1
=1
Chúc bạn học tốt nha
48.13 + 61 . 16
= 48 . ( 10 + 3 ) + ( 60 + 1 ) . 16
= [ 48 . 10 + 48.3 ] + [ 60 . 16 + 1 . 16 ]
= 624 + 976
= 1600
1, \(48.13+61.16=16.3.13+61.16=16.\left(39+61\right)=16.100=1600\)
\(2,5.6.32+60.15.2+3.16.5=5.6.2.16+60.15.2+3.5.4.4=60.16+60.30+60.4=60.\left(16+30+4\right)=60.50=3000\)
a)=1/2 . 8/15 - 3/4.47/9
=4/15 - 47/12
=-73/20
b)=2-1/3 . -21/20
=2+7/20
=47/20
b)3.(-5)2+2.(-5)-20 => 3.(--5).(-5)+2.(-5)-20
= (-5)(3.-5+2)-20
=(-5)(-13)-20
= 65-20=45
\(a,5.\left(-8\right).2.\left(-3\right)\)
\(=-40.\left(-6\right)=-240\)
\(b,3.\left(-5\right)^2+2.\left(-5\right)-20\)
\(=4.25-10-20\)
\(=100-10-20=70\)
Ta có :A = \(\frac{5}{3.4}+\frac{5}{4.6}+\frac{5}{5.8}+...+\frac{5}{40.78}=\frac{5}{2.2.3}+\frac{5}{2.3.4}+\frac{5}{2.4.5}+...+\frac{5}{2.39.40}\)
\(=\frac{5}{2}\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{39.40}\right)=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{39}-\frac{1}{40}\right)\)
\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{40}\right)=\frac{5}{2}.\frac{19}{40}=\frac{19}{16}\)