5+10+15+...+105+310.
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\(\left(x-3\right)^2=\left(x-3\right)^3\Leftrightarrow\left(x-3\right)^3-\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(x-3\right)^2\left[x-3-1\right]=0\Leftrightarrow\left(x-3\right)^2\left(x-4\right)=0\Leftrightarrow x=3;x=4\)
\(10-\left\{\left[\left(x:4+15\right):10+3.2^4\right]:10\right\}=5\)
\(\Leftrightarrow\left[\left(\dfrac{x}{4}+15\right):10+3.16\right]:10=5\)
\(\Leftrightarrow\left(\dfrac{x}{4}+15\right):10+48=50\Leftrightarrow\left(\dfrac{x}{4}+15\right):10=2\Leftrightarrow\dfrac{x}{4}+15=20\)
\(\Leftrightarrow x=20\)
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Dat \(S=5+10+15+...+310=5x\left(1+2+3+...+62\right)=5x\frac{\left(62+1\right)x62}{2}=9765\)
cach 2
\(S=\frac{\left(310+5\right)x62}{2}=9765\)
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Số số hạng là:
( 105 - 5 ) : 5 + 1 = 21 ( SỐ HẠNG)
Tổng là:
( 105 + 5 ) : 2 x 21 = 1155
Đáp số: 1155
Số số hạng là:
( 105 - 5 ) : 5 + 1 = 21 ( SỐ HẠNG)
Tổng là:
( 105 + 5 ) : 2 x 21 = 1155
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(\Leftrightarrow\left(\dfrac{x+2001}{5}+1\right)+\left(\dfrac{x+1999}{7}+1\right)+\left(\dfrac{x+1997}{9}+1\right)+\left(\dfrac{x+1995}{11}+1\right)=0\)
=>x+2006=0
=>x=-2006
b: \(\Leftrightarrow\left(\dfrac{x-15}{100}-1\right)+\left(\dfrac{x-10}{105}-1\right)+\left(\dfrac{x-100}{5}-1\right)=\left(\dfrac{x-100}{15}-1\right)+\left(\dfrac{x-105}{10}-1\right)+\left(\dfrac{x-110}{5}-1\right)\)
=>x-105=0
=>x=105
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a)75*2014+2015*24+1990=75*2015-75+2015*24+2015-25=2015*(75+24+1)-100=2015*100-100=201500-100=201400
b)Số các số hạng là:(310-5):5+1=62
Ta có:5+10+15+20+.......+300+305+310=(5+310)+(10+305)+...+(15+300)=315*62=19530