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a) 5^2018:2^2015-6^2+2017^0
=5^3-36+1
=125-36+1
=89+1=90
b)12:{390:[500-(5^3+35.7)]}
=12:{390:[500-(125+245)]}
=12:{390:[500-370]}
=12:{390:130}
=12:3=4
Hok tốt
\(a)\left(-\dfrac{3}{4}\div\dfrac{2}{-3}\right)\times\dfrac{-5}{7}\)
\(=\dfrac{9}{8}\times\dfrac{-5}{7}\)
\(=\dfrac{-45}{56}\)
\(b)\dfrac{-2}{-5}\div\left(\dfrac{7}{-5}\div\dfrac{-3}{2}\right)\)
\(=\dfrac{2}{5}\div\left(\dfrac{7}{-5}\div\dfrac{-3}{2}\right)\)
\(=\dfrac{2}{5}\div\dfrac{14}{15}\)
\(=\dfrac{3}{7}\)
A = 1 + 2 + 3 + ... + 2018
= ( 1 + 2018 ) + ( 2 + 2017) + ... + ( 1009 + 1010 )
= 2019 + 2019 + ... + 2019 ( có 1009 số 2019 )
= 2019 x 1009 = 2037171
B = 1 + 3 + 5 + ... + 2017
= ( 1 + 2017 ) + ( 3 + 2015 ) + ... + ( 1007 + 1010) + 1009
= 2018 + 2018 + ... + 2018 + 1009 (có 504 số 2018)
= 2018 x 504 + 1009 = 1018081
Còn lại làm giống ý trên .
\(=>M=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{2020}{2019}\)
\(=>M=\frac{2020}{2}=1010\)
\(M=\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2018}\right)\left(1+\frac{1}{2019}\right)\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2019}{2018}.\frac{2020}{2019}\)
\(=\frac{2020}{2}\)
\(=1010\)
Study well ! >_<
a) c1 := -2/-5+-5/-6+4/5
=2/5+5/6+4/5
=12/30+25/30+24/30
=61/30
c2:=(2/5+4/5)+4/5
=(2/5+4/5)+5/6
=6/5+5/6
=36/30+25/30
=61/30
b)c1:=-3/-4+11/-15+-1/2
=3/4+-11/15+-1/2
=45/60+-44/30+-30/60
-29/30
c2:=3/4+(-11/15+-1/2)
=(3/4+-1/2)+-11/15
=(3/4+-2/4)+-11/5
=1/4+-11/15
=15/60+-44/60
=-29/60
2,
a) \(315-\left(135-x\right)=215\)
\(\Rightarrow135-x=315-215\)
\(\Rightarrow135-x=100\)
\(\Rightarrow x=135-100\)
\(\Rightarrow x=35\)
b) \(x-320:32=25\cdot16\)
\(\Rightarrow x-10=5^2\cdot4^2\)
\(\Rightarrow x-10=20^2\)
\(\Rightarrow x-10=400\)
\(\Rightarrow x=410\)
c) \(3\cdot x-2018:2=23\)
\(=3\cdot x-1009=23\)
\(\Rightarrow3\cdot x=1032\)
\(\Rightarrow x=1032:3\)
\(\Rightarrow x=344\)
d) \(280-9\cdot x-x=80\)
\(\Rightarrow280-x\cdot\left(9+1\right)=80\)
\(\Rightarrow280-10\cdot x=80\)
\(\Rightarrow10\cdot x=280-80\)
\(\Rightarrow10\cdot x=200\)
\(\Rightarrow x=20\)
e) \(38\cdot x-12\cdot x-x\cdot16=40\)
\(\Rightarrow x\cdot\left(38-12-16\right)=40\)
\(\Rightarrow x\cdot10=40\)
\(\Rightarrow x=40:10\)
\(\Rightarrow x=4\)
B = 52 + 53 + 54 +....+52018
5B = 53 + 54+......+52018 + 52019
5B - B = 52019 - 52
4B = 52019 - 52
B = ( 52019 - 52): 4
\(B=5^2+5^3+5^4+....+5^{2018}\)
\(\Leftrightarrow5B=5^3+5^4+5^5+....+5^{2018}\)
\(\Leftrightarrow4B=5^{2018}-5^2\)
\(\Leftrightarrow B=\dfrac{5^{2018}-5^2}{4}\)