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\(1,\frac{1212}{1515}+\frac{1212}{3535}+\frac{1212}{6363}+\frac{1212}{9999}=\frac{12}{15}+\frac{12}{35}+\frac{12}{63}+\frac{12}{99}=6\left(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\right)=6\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right).Tacocongthuc:\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\Rightarrow\frac{1212}{1515}+\frac{1212}{3535}+\frac{1212}{6363}+\frac{1212}{9999}=6\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-.....-\frac{1}{11}\right)=6\left(\frac{1}{3}-\frac{1}{11}\right)=\frac{48}{33}=\frac{16}{11}\)
\(2,\left(x+1\right)+\left(x+2\right)+.....+\left(x+211\right)=211x+\left(1+2+....+211\right)=211x+\frac{212.211}{2}=211x+22366=23632\Leftrightarrow211x=23632-22366=1266\Leftrightarrow x=6\)
a, \(14:\left(4\frac{2}{3}:1\frac{5}{9}\right)+14:\left(\frac{2}{3}+\frac{8}{9}\right)\)
=> \(14:\frac{28}{9}+14:\frac{14}{9}=>14.\frac{9}{28}+14.\frac{9}{14}\)
=> 14. ( \(\frac{9}{28}+\frac{9}{14}\) )
=> \(14.\frac{27}{28}=\frac{419}{28}\)
b, \(\frac{1212}{1515}+\frac{1212}{3535}+\frac{1212}{6363}+\frac{1212}{9999}\)
=> \(\frac{4}{5}+\frac{12}{35}+\frac{4}{21}+\frac{4}{33}\)
=> \(\frac{8}{7}+\frac{24}{77}=\frac{16}{11}\)
bài 2 :
( x + 1 ) + ( x + 2 ) + ... + ( x + 211 ) = 23632
=> ( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 211 ) = 23632
=> 211x + 22366 = 23632
=> 211x = 23632 - 22366
=> 211x = 1266
=> x = 1266 : 211
x = 6
1. 28 :2x = 7
14 . x = 7
=> x = 14 . 7 =98
2. (115 + 3x ) - (17 + x) = 214
115 + 3x - 17 - x = 214
115 - 17 + 3x - x = 214
98 + 2x = 214
2x = 214 - 98 = 116
x = 116 : 2 = 58
a) \(1-2+3-4+...+213-214\)
\(=\left(1-2\right)+\left(3-4\right)+...+\left(213-214\right)\)(có 107 cặp)
\(=\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)
\(=-107\)
b) \(\left|x-17\right|+13=25\)
\(\Rightarrow\left|x-17\right|=25-13\)
\(\Rightarrow\left|x-17\right|=12\)
\(\Rightarrow\left[{}\begin{matrix}x-17=12\\17-x=12\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=12+17\\-x=12-17\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=29\\-x=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=29\\x=5\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=29\\x=5\end{matrix}\right.\)
\(1-2+3-4+5-6+...+213-214\)
\(=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(213-214\right)\)
\(=\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)
\(=\left(-1\right)\left[\left(\dfrac{214-1}{1}+1\right):2\right]\)
\(=-1.107\)
\(=-107\)
\(\left|x-17\right|+13=25\)
\(\Rightarrow\left|x-17\right|=12\)
\(\Rightarrow\left[{}\begin{matrix}x-17=12\\x-17=-12\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=29\\x=5\end{matrix}\right.\)
x:0,25+x:0,01+x:0,5+x=214
\(\Rightarrow x\times4+x\times100+x\times2+x=214\)
\(\Rightarrow x\times\left(4+100+2+1\right)=214\)
\(\Rightarrow x\times107=214\)
\(\Rightarrow x=214:107\)
\(\Rightarrow x=2\)
x:0.25+x:0.01+x:0.5+x=214
x:(0.25+0.01+0.5+1)=214
x:1.76=214
x=214*1.76
x=376.64
a) - (4x - 25) + (214 + 2x) = - x + 213
<=> - 4x + 25 + 214 + 2x = - x + 213
<=> - 2x + 239 = -x + 213
<=> - x = - 2x + 26
<=> 2x - 26 = x
<=> x = 26
b) (x + 2).(x - 7) = 0
<=> x + 2 = 0
hoặc x - 7 = 0
<=> x = - 2
hoặc x = 7
c) x3 - 2x2 = 0
<=> x3 = 2x2
<=> x2.x = 2x2
<=> x = 2
a) x ÷ 0.25 + x + x + 0.1 = 214
x. 4 + x + x = 214 - 0.1
x. 6 = 213.9
x = 213.9 ÷ 6
x = 35.65
Vậy,...
b) 17.75 - ( 0.5 × x ÷ 2 - 4.27 ) = 15
0.5 × x ÷ 2 - 4.27 = 17.75 ÷ 15
0.5 × x ÷ 2 - 4.27 = \(\frac{71}{60}\)
0.5 × x ÷ 2 = \(\frac{71}{60}+4.27\)
0.5 × x ÷ 2 = \(\frac{409}{75}\)
0.5 × x = \(\frac{409}{75}×2\)
0.5 × x = \(\frac{818}{75}\)
x = \(\frac{818}{75}\div0.5\)
x = \(\frac{1636}{75}\)
Vậy,...
Cbht. Phần b mình không chắc nhé
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+214\right)=23632\)
\(\Rightarrow\left(x+x+.....+x\right)+\left(1+2+....+214\right)=23632\)
\(\Rightarrow214x+23005=23632\)
\(\Rightarrow214x=627\)
\(\Rightarrow x=\frac{627}{214}\)
kq y em mà thấy kì nên bấm bỏ