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Ta có: (x+1)+(x+2)+...+(x+2013)=2013.2014
<=>2013x+2027091=4054182
<=>2013x=2029091
<=>x=1007
(x+1) + (x+2) + ..........+ (x+2013) = 4054182
x+1 + x+2 + ..........+ x+2013 = 4054182
(x+x+x+x+..........+x) + (1+2+3+4+..........+2013) = 4054182
2013x + (1+2013) . 2013 : 2 = 4054182
2013x + 2027091 = 4054182
2013x = 4054182 - 2027091
2013x = 2027091
x = 2027091 : 2013
x = 1007
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$2015=5.13.31$2015=5.13.31
Ta có: $1.2.....1007=1.2...5....13.....31...1007\text{ chia hết cho }5.13.31=2015$1.2.....1007=1.2...5....13.....31...1007 chia hết cho 5.13.31=2015
$1008.1009.....2004=1008....\left(1010\right)....\left(1014\right)...\left(1023\right)....2004$1008.1009.....2004=1008....(1010)....(1014)...(1023)....2004
$=1008....\left(5.202\right)....\left(13.78\right)....\left(31.33\right)...2004\text{ chia hết cho }5.13.33=2015$=1008....(5.202)....(13.78)....(31.33)...2004 chia hết cho 5.13.33=2015
Do đó tổng 2 số trên chia hết cho 2015.
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Ta có :
\(\frac{10^{20}+1}{10^{21}+1}< \frac{10^{20}+1+9}{10^{21}+1+9}=\frac{10^{20}+10}{10^{21}+10}=\frac{10\left(10^{19}+1\right)}{10\left(10^{20}+1\right)}=\frac{10^{19}+1}{10^{20}+1}\)
Vậy \(\frac{10^{19}+1}{10^{20}+1}>\frac{10^{20}+1}{10^{21}+1}\)
=>2013x+[(2013+1).2013:2)]=4054182
=>2013x+2027091=405182
=>2013x=405182-2027091=2027091
=>x=2027091:201
=>x=1007
có đúng ko đấy hay lại sai ngớ ngẩn
những cung cảm ơn vì khá là nhanh kết bạn đê