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a) (417+64):(416+16)
= (417+43):(416+42)
=420:418
=42=16
b)83:24+513:511.30
=(23)3:24+52.1
=26:24+25
=22+25
=4+25=29
c)33.48+34.42+81.42
=33.48+33.3.42+33.3.42
=33.48+33.126+33.126
=33.(48+126+126)
=27.300
=8100
1.
\(B=20182018.2017-20172017.2018\)
\(B=2018.10001.2017-2017.10001.2018\)
\(B=0\)
1 B=20182018.2017-20172017.2018
B=2018.10001.2017-2017.10001.2018
B=0
2 C=12+22+32+...+1002
C=1(1+0)+2(1+1)+3(1+2)+...+100(1+99)
C=1+2+1.2+3+2.3+...+100+99.100
C=(1+2+3+...+100)+(1.2+2.3+...+99.100)
C=[(1+100).100:2]+[(99.100.101):3]
C=5050+333300
C=338350
\(-23\cdot63+23\cdot21-58\cdot23\)
\(=23\left(-63+21-58\right)\)
\(=23\cdot\left(-100\right)\)
\(=-2300\)
-3/11.(-22)/66.121/15
=(-3).(-22).121
11.66.15
=11
15
3/7.2/5.7/3.20.19/72
=3.2.7.20.19
7.5.3.72
=76
16
6/7.8/13+6/13.9/7-3/13.6/7
=6/7.8/13+6/7.9/13-3/13.6/7
=6/7.(8/13+9/13-3/13)
=6/7.14/13
=12/13
-1/4.152/11+68/4.(-1)/11
=152/4.(-1)/11+68/4.(-1)/11
=(-1)/11.(152/4+68/4)
=(-1)/11.220/4
=-110/22
-5/7.2/11+(-5)/7.9/11+12/7
=-5/7.2/11+-5/7.9/11+12/7
=-5/7.(2/11+9/11)+12/7
=-5/7.1+12/7
=(-5)/7+12/7
=7/7
=1
146/13-(18/7+68/13)
=146/13-18/7-68/13
=(146/13-68/13)-18/7
=78/13-18/7
=6-18/7
=42/7-18/7
=24/7
\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{997.999}\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{997.999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{997}-\frac{1}{999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(1-\frac{1}{999}\right)=\frac{5}{2}.\frac{998}{999}=\frac{2495}{999}=2\frac{497}{999}\)
\(A=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}\)
\(\Leftrightarrow A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(1-\frac{1}{16}\right)=\frac{2}{3}.\frac{15}{16}=\frac{5}{8}\)
C = 5/1x3 + 5/3x5 + 5/5x7 + ... + 5/997x999
C = 5 - 5/3 + 5/3 - 5/5 + 5/5 - 5/7 + ... + 5/997 - 5/999
C = 5 - 5/999
C = bạn tự tính nhé !
A = 2/4 + 2/28 + 2/70 + 2/130 + 2/208
A = 2/1x4 + 2/4x7 + 2/7x10 + 2/10x13 + 2/13x16
A = 2 - 2/4 + 2/4 - 2/7 + 2/7 - 2/10 + 2/10 - 2/13 + 2/13 - 2/16
A = 2 - 2/16
A = bạn tự tính nhé !
B = ( 1024 . 10 . 15625 + 9765625 . 256 ) : ( 256 . 625+78125 . 32 )
=( 160000000+2500000000 ):( 160000+2500000)
= 2660000000 : 2660000
= 1000
B = ( 1.024 . 10 . 15.625 + 9.765.625 . 256 ) : ( 256 . 625+78125 . 32 )
B =( 160.000.000+2.500.000.000 ):( 160.000+2.500.000)
B = 2.660.000.000 : 2.660.000
B = 1.000