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\(\left[9-\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\right)\right]\div\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{9}{10}\right)\)
\(=\left[\left(1+1+1+...+1\right)-\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\right)\right]\div\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{9}{10}\right)\)
có 9 số 1 có 9 số hạng
\(=\left[\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{3}\right)+\left(1-\frac{1}{4}\right)+...+\left(1-\frac{1}{10}\right)\right]\div\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{9}{10}\right)\)
\(=\left[\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{9}{10}\right]\div\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{9}{10}\right)\)
\(=1\)
\(a,3x\left(x-\frac{2}{3}\right)=0
\)
\(\)TH1:
3x=0
x=0:3
x=0
TH2
\(x-\frac{2}{3}=0
\)
\(x=0+\frac{2}{3}=\frac{2}{3}\)
Vậy x={0;\(\frac{2}{3}\)}
34 +14 :x=25
\(\frac{1}{4}:x=\frac{2}{5}-\frac{3}{4}\)
\(x=\frac{1}{4}:-\frac{7}{20}\)
\(x=-\frac{20}{28}\)
\(x=-\frac{5}{7}\)
Đặt \(A=1.2+2.3+3.4+...+n\left(n+1\right)\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+3n\left(n+1\right)\)
\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+n\left(n+1\right)\left(n+2-n+1\right)\)
\(=1.2.3+2.3.4-1.2.3+...+n\left(n+1\right)\left(n+2\right)-\left(n-1\right)n\left(n+1\right)\)
\(=n\left(n+1\right)\left(n+2\right)\)
\(\Rightarrow1.2+2.3+3.4+...+n\left(n+1\right)=\frac{n\left(n+1\right)\left(n+2\right)}{3}\)
[ 212 + ( 48 - 2 . x . x2 ) : 40 - 3 = 3
[ 212 + ( 48 - 2 . x . x2 ) : 40 = 3 + 3 = 6
[ 212 + ( 48 - 2 . x . x2 ) = 6 . 40 = 240
=> 48 - 2 . x . x2 = 240 - 212 = 28
2 . x . x2 = 48 - 28 = 20
x. x2 = 20 : 2 = 10
\(\Rightarrow S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+..+\frac{1}{n^2}-\frac{1}{n+1^2}\)
\(\Rightarrow S=1-\frac{1}{n+1}\)
\(\Rightarrow S+\frac{n}{n+1}\)