tinh \(1+1+2.15+1+3\left(23456.7968798.\left(234233-234233\right)\right)\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
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\(VT=\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+...+\frac{1}{\left(x+3\right)\left(x+4\right)}\)
\(=\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+...+\frac{1}{x+3}-\frac{1}{x+4}\)
\(=\frac{1}{x}-\frac{1}{x+4}=\frac{x+4-x}{x\left(x+4\right)}=\frac{4}{x\left(x+4\right)}\)
\(\Rightarrow\frac{4}{x\left(x+4\right)}=\frac{m}{x\left(x+4\right)}=VP\Rightarrow m=4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
B=\(\dfrac{1}{\left|x-2\right|+3}\)
do \(\left|x-2\right|\ge0\forall x\)
=> \(\left|x-2\right|+3\ge3\)
=> \(\dfrac{1}{\left|x-2\right|+3}\le\dfrac{1}{3}\)
=> B \(\le\dfrac{1}{3}\)
GTLN của B =\(\dfrac{1}{3}\)
khi x-2=0
=> x=2
vậy GTLN của A=\(\dfrac{1}{3}\) khi x=2
![](https://rs.olm.vn/images/avt/0.png?1311)
(1-1/3)x(1-1/5)x(1-1/7)x(1-1/9)x(1-1/2)x(1-1/4)x(1-1/6)x(1-1/8)x(1-1/10)
=2/3x4/5x6/7x8/9x1/2x3/4x5/6x7/8x9/10
=2x4x6x8x1x3x5x7x9 /3x5x7x9x2x4x6x8x10
=1/10
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)\)
=\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{99}{100}\)
=\(\frac{1.2.3...99}{2.3.4...100}\)
=\(\frac{1}{100}\)
Chúc bạn học giỏi nha
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P=\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}=\left(\frac{4}{11}+\frac{3}{22}\right)+\left(\frac{5}{2}+\frac{1}{30}+\frac{13}{60}\right)=\frac{1}{2}+\frac{11}{4}=\frac{13}{4}\)
\(Q=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}=\frac{1.2.3....19}{2.3.4....20}=\frac{1}{20}\)
1+1+2.15+1+3(23456.7968798.(234233-234233))
=2+30+1+3(23456.7968798.0)
=33+3.0
=33
1+1+2.15+1+3(23456.7968798.(234233-234233))
=2+30+1+3(23456.7968798.0)
=33+3.0
=33