tính nhanh
20 + 80 + 11 + 89
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\(S=20+25+30+...+75+80\\ =\left(80+20\right)+\left(25+75\right)+\left(30+70\right)+...+50\\ =100+100+100+100+...+50\\ =6.10+50=650\)
Giải:
\(20+25+30+35+...+80\)
Số số hạng: \(\left(80-20\right):5+1=13\)
Tổng dãy: \(\left(20+80\right).13:2=650\)
\(\dfrac{x+2}{89}+\dfrac{x+5}{86}>\dfrac{x+8}{83}+\dfrac{x+11}{80}\)
\(\Leftrightarrow\dfrac{x+2}{89}+1+\dfrac{x+5}{86}+1>\dfrac{x+8}{83}+1+\dfrac{x+11}{80}+1\)
\(\Leftrightarrow\dfrac{x+91}{89}+\dfrac{x+91}{86}>\dfrac{x+91}{83}+\dfrac{x+91}{80}\)
\(\Leftrightarrow\dfrac{x+91}{89}+\dfrac{x+91}{86}-\dfrac{x+91}{83}-\dfrac{x+91}{80}>0\)
\(\Leftrightarrow\left(x+91\right)\left(\dfrac{1}{89}+\dfrac{1}{86}-\dfrac{1}{83}-\dfrac{1}{80}\right)>0\)
Ta có: \(\dfrac{1}{89}+\dfrac{1}{86}+\dfrac{1}{83}+\dfrac{1}{80}< 0\)
\(\Leftrightarrow x+91< 0\)
\(\Leftrightarrow x< -91\)
Vậy...........
11 x 10 + 89 x 5 + 89 x 3 + 89 x 2
= 110 + 89 x ( 5 + 3 + 2)
= 110 + 89 x 10
= 110 + 890
= 1000
`a)79+65 = 79 + (21+44)=(79+21)+44=100+44=144`
`b) 996 + 45 = 996+(41+4)=(996+4)+41=1000+41=1041`
`c) 37 + 198 = (35+2)+198=35+(2+198)=35+200 = 235`
`c) 3492 + 319 = 3492+(311+8)=(3492+8)+311=3500+311=3811`
a) 79+65=(79+21)+44=100+44=144
b) 996+45=(996+4)+41=1000+41=1041
\(\dfrac{x+2}{89}+\dfrac{x+5}{86}>\dfrac{x+8}{83}+\dfrac{x+11}{80}\)
\(\Leftrightarrow\dfrac{x+91}{89}+\dfrac{x+91}{86}>\dfrac{x+91}{83}+\dfrac{x+91}{80}\)
\(\Leftrightarrow\left(x+91\right)\left(\dfrac{1}{89}+\dfrac{1}{86}\right)>\left(x+91\right)\left(\dfrac{1}{83}+\dfrac{1}{80}\right)\)
Mà \(\dfrac{1}{89}+\dfrac{1}{86}< \dfrac{1}{83}+\dfrac{1}{80}\)
Nên \(x+91< 0\Leftrightarrow x< -91\)
20 + 80 + 11 + 89
= 100 + 100
= 200
20+80+11+89=200