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\(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{200}\right)\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1+\dfrac{1}{200}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{199}{200}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{201}{200}\)
=1/200*201/2=201/400>200/400=1/2
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a: 2x(x+1)-135=-200
=>2(x^2+x)=-65
=>2x^2+2x+65=0
=>x^2+x+32,5=0
=>x^2+x+0,25+32,25=0
=>(x+0,5)^2+32,25=0(vô lý)
b: 4x-5(x-1)+15=13
=>4x-5x+5=-2
=>5-x=-2
=>x=5+2=7
c: 2/3x-1/4=3/5-7/8
=>2/3x=3/5-7/8+1/4=24/40-35/40+10/40=-1/40
=>x=-1/40:2/3=-1/40*3/2=-3/80
d: 1/2(2x-3)+105/2=-137/2
=>1/2(2x-3)=-137/2-105/2=-242/2=-121
=>2x-3=-242
=>2x=-239
=>x=-239/2
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= 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/x - 1/x + 1
= 1/2 - 1 /x + 1 =199/200
=1/x+1 = 1/2 - 199/200
1/ x + 1 = ....
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{x.\left(x+1\right)}=\frac{199}{200}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{199}{200}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{199}{200}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{199}{200}\)
\(\Rightarrow\frac{1}{x+1}=-\frac{99}{200}\)
\(\Rightarrow\frac{-99}{-\left(x+1\right).99}=\frac{-99}{200}\)
\(\Rightarrow-99x+-99=200\)
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\(x-1\in\left\{1;6;2;3;-1;-6;-2;-3\right\}\)
\(\Leftrightarrow x\in\left\{2;7;3;4;0;-5;-1;-2\right\}\)
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\(C=\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times...\times\frac{199}{200}\)
\(C^2=\left(\frac{1}{2}\right)^2\times\left(\frac{3}{4}\right)^2\times\left(\frac{5}{6}\right)^2\times...\times\left(\frac{199}{200}\right)^2\)
\(< \frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times...\times\frac{199}{200}\times\frac{200}{201}\)
\(=\frac{1}{201}< \frac{1}{196}\)
\(\Rightarrow C< \sqrt{\frac{1}{196}}=\frac{1}{14}\)
giúp mình vs
\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-199}{200}=-\dfrac{1}{200}\)