tinh chi vay

a,A=4/2.4+4/4.6+4/6.8+......+4/2012.2014

\(\Rightarrow\frac{1}{2}A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{2012\cdot2014}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2012}-\frac{1}{2014}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{2014}\)

\(\Rightarrow A=1-\frac{1}{1007}\)

\(\Rightarrow A=\frac{1006}{1007}\)

2013${}^{}$-2012.2014.(2013${}^{}$+1)

=2013⁴-(2013-1)(2013+1).(2013²+1)

=2013⁴-(2013²-1)(2013²+1)

=2013⁴-2013⁴+1

=1

A = \(\frac{1}{2.4}+\frac{1}{4.6}+....+\frac{1}{2012.2014}\)

A = \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2012}-\frac{1}{2014}\right)\)

A = \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2014}\right)\)

A = \(\frac{1}{2}.\frac{503}{1007}\)

A = \(\frac{503}{2014}\)

2A=\(\frac{4-2}{2.4}+\frac{6-4}{4.6}+...+\frac{2014-2012}{2012.2014}\)

\(2A=\frac{4}{2.4}-\frac{2}{2.4}+\frac{6}{4.6}-\frac{4}{4.6}+...+\frac{2014}{2012.2014}-\frac{2012}{2012.2014}\)

\(2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2012}-\frac{1}{2014}\)

\(2A=\frac{1}{2}-\frac{1}{2014}=\frac{503}{1007}\Rightarrow A=\frac{503}{2014}\)

help

ét ô ét

a=2013.(2012+1)=2013.2012+2013

b=2012.2014=2012.(2013+1)=2012.2013+2012

Vì 2013>2012
=>a>b

Ta có \(2y^2⋮2\Rightarrow x^2\equiv1\left(mod2\right)\Rightarrow x^2\equiv1\left(mod4\right)\Rightarrow2y^2⋮4\Rightarrow y⋮2\Rightarrow x^2\equiv5\left(mod8\right)\) (vô lí).

Vậy pt vô nghiệm nguyên.

2: \(PT\Leftrightarrow3x^3+6x^2-12x+8=0\Leftrightarrow4x^3=\left(x-2\right)^3\Leftrightarrow\sqrt[3]{4}x=x-2\Leftrightarrow x=\dfrac{-2}{\sqrt[3]{4}-1}\).