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-(127+38-21)-(121-27+48)+50
=-127-38+21-121+27-48+50
=(-127+27)-(38+48)+(21-121)+50
=-100-86-100+50
=-(100+100+86)+50
=-286+50
=-236
-39+(193-127+96)-(193+196-127)
=-39+193-127+96-193-196+127
=-39+(193-193)-(127+127)+(96-196)
=-39-100
=-139
a)=3/4 -3/2+1/2 *12/5=3/4 -3/2 +6/5=30/40 -60/40 +48/40=9/20 b)75/287 c)1
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2011}-\frac{1}{2012}+\frac{1}{2013}\)
\(S=\left(1+\frac{1}{3}+\frac{1}{5}+.....+\frac{1}{2011}+\frac{1}{2013}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2012}\right)\)
\(S=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2012}\right)\)
\(S=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+..+\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}-\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{1006}\right)\)
\(S=\frac{1}{1007}+\frac{1}{1008}+.....+\frac{1}{2012}+\frac{1}{2013}=P\)
=>S-P=0
=>(S-P)2016=0
Câu a )
S = 5 + 52 +..... + 52012
=> S \(⋮5\)
S = 5 + 52 +..... + 52012
S = ( 5 + 53 ) + ( 52 + 54 ) + ........ + ( 52010 + 52012 )
S = 5 ( 1 + 52 ) + 52 ( 1 + 52 ) + ......... + 52010 ( 1 + 52 )
S = 5 x 26 + 52 x 26 + ................ + 52010 x 26
S = 26 ( 5 + 52 + .... + 52010 )
=> S\(⋮26\)
=>\(S⋮13\)( do 26 = 13 x 2 )
Do ( 5 , 13 ) = 1
=> \(S⋮5x13\)
=> \(S⋮65\)
a) \(\left(1^2+2^2+3^2+....+2012^2\right).\left(91-273:3\right)\)
\(=\left(1^2+2^2+3^2+...+2012^2\right).\left(91-91\right)\)
\(=0\)
b) \(\left(-284\right).172+\left(-284\right).\left(-72\right)=\left(-284\right).\left(172+-72\right)\)
\(=\left(-284\right).100\)
\(=-28400\)
c) \(\frac{1}{5}+\frac{-1}{6}+\frac{1}{7}+\frac{-1}{8}+\frac{1}{9}+\frac{1}{8}+\frac{-1}{7}+\frac{1}{6}+\frac{-1}{5}\)
\(=\left(\frac{1}{5}+\frac{-1}{5}\right)+\left(\frac{1}{6}+\frac{-1}{6}\right)+\left(\frac{1}{7}+\frac{-1}{7}\right)+\left(\frac{1}{8}+\frac{-1}{8}\right)+\frac{1}{9}\)
\(=0+0+0+0+\frac{1}{19}\)
= 0
\(\left(75\%+\frac{1}{2}\right)\text{ : }\left|-1\frac{1}{2}\right|-\frac{5}{27}\cdot1,8\cdot2012^0\)
\(=\left(\frac{3}{4}+\frac{1}{2}\right):\left|-\frac{3}{2}\right|-\frac{5}{27}\cdot\frac{9}{5}\)
\(=\frac{5}{4}\text{ : }\frac{3}{2}-\frac{1}{3}\)
\(=\frac{5}{6}-\frac{1}{3}\)
\(=\frac{1}{2}\)
\(\left(75\%+\frac{1}{2}\right)-\left|-1\frac{1}{2}\right|-\frac{5}{27}\cdot1,8\cdot2012^0\)
\(=\left(\frac{75}{100}+\frac{1}{2}\right)-\left|-\frac{3}{2}\right|-\frac{5}{27}\cdot\frac{9}{5}\cdot1\)
\(=\left(\frac{3}{4}+\frac{1}{2}\right)-\frac{3}{2}-\frac{5}{27}\cdot\frac{9}{5}\)
\(=\left(\frac{3}{4}+\frac{2}{4}\right)-\frac{3}{2}\cdot\frac{1}{3}\)
\(=\frac{5}{4}-\frac{1}{2}=\frac{5}{4}-\frac{2}{4}=\frac{3}{4}\)
Ez mà :)))