\title{Comparación de sucesiones}
\language{en}
\range{-3..3}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{yes}
\format{html}
\precision{10000}

\text{n=<i>n</i>}
\text{seq1=<i>u<sub>n</sub></i>}
\text{seq2=<i>v<sub>n</sub></i>}
\integer{lim1=random(2..25)}
\integer{lim2=\lim1+random(2..20)}
\text{abs1=| \seq1 - \lim1 |}
\text{abs2=| \seq2 - \lim2 |}
\text{abs12=| \seq1 - \lim2 |}
\text{abs21=| \seq2 - \lim1 |}
\integer{coeff1=random(2..9)}
\integer{coeff2=random(2..9)}
\integer{coeff2=\coeff2=\coeff1?\coeff1+1}
\integer{Lim1=\lim1*\coeff1}
\integer{Lim2=\lim2*\coeff2}
\text{spc=&nbsp;&nbsp;&nbsp;}
\integer{start=random(1..8)*random(100,1000,10000,100000)}
\text{ch=random(par,impar, divisible por 3, divisible por 5, divisible por 10,
no divisible por 3, no divisible por 5, no divisible por 10)}
\text{cond1=random(\n&gt;\start,todo \n)}

\text{conds=\coeff1\abs2 &lt; \coeff2\abs1\spc para \cond1,
	\coeff1\abs2 &gt; \coeff2\abs1\spc para \cond1,
	\coeff1\abs21 &lt; \coeff2\abs12\spc para \cond1,
	\coeff1\abs21 &gt; \coeff2\abs12\spc para \cond1,
	\coeff1\abs2 &lt; | \coeff2\seq1 - \Lim1 |\spc para \cond1,
	
	| \coeff1\seq2 - \Lim2 | &lt; \coeff2\abs1\spc para \cond1,
	-\coeff1\abs2 &lt; \coeff2\abs1\spc para \cond1,
	\coeff1\abs2 &lt; -\coeff2\abs1\spc para \cond1,
	-\coeff1\abs2 &lt; -\coeff2\abs1\spc para \cond1,
	-\coeff1\abs2 &gt; -\coeff2\abs1\spc para \cond1,
	
	\coeff2\abs2 &lt; | \coeff1\seq1 - \Lim1 |\spc para \cond1,
	| \coeff2\seq2 - \Lim2 | &lt; \coeff1\abs1\spc para \cond1,
	\coeff1\abs2 &lt; \coeff2\abs1\spc para \n&lt;\start,
	\coeff1\abs21 &gt; \coeff2\abs12\spc para \n&lt;\start,
	\coeff1\abs2 &lt; \coeff2\abs1\spc para todo \n \ch,
	
	\coeff1\abs21 &gt; \coeff2\abs12\spc para todo \n \ch
	
}
\text{liml=\lim2,\lim2,\lim1,\lim1,\lim2,
	\lim2,\lim2,\lim2,\lim2,\lim2,
	\lim2,\lim2,\lim2,\lim1,\lim2,
	\lim1
}
\integer{cnt=items(\conds)}
\integer{t=random(1..\cnt)}
\real{lim=item(\t,\liml)}
\text{cond=item(\t,\conds)}
\text{non=La convergencia no puede ser determinada}
\text{cv=Converge hacia \lim}
\text{cvdiff=Converge hacia \lim2 - \lim1}
\text{dv=No converge hacia \lim}
\text{vide=(\seq2) no existe}
\text{goods=\cv,\non,\non,\dv,\non,
	\dv,\non,\vide,\non,\cv,
	\cv,\cv,\non,\non,\non,
	\dv,
}
\text{bads=\non,\cv,\cv,\non,\cv,
	\cv,\cv,\non,\cv,\non,
	\non,\Lim2,\cv,\dv,\cv,
	\non,
}
\text{good=item(\t,\goods)}
\text{bad1=item(\t,\bads)}

\text{lims=\bad1,\non,\cv,\dv,\cvdiff,\vide
}

\statement{Sean (\seq1) y (\seq2) dos sucesiones de números reales donde
(\seq1) converge hacia \lim1. Si tenemos
<p><center>\cond ,
</center> <p>
¿Qué se puede decir acerca de la convergencia de (\seq2)?
(Debes elegir la mejor opción.)
}

\choice{Su respuesta es}{\good}{\lims}
