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

\real{a=randint(20..80)/100}
\integer{big=random(0,0,0,1)}
\real{a=\big=1?\a+randint(1..5)}
\integer{inverse=\big=0?random(0,1):1}
\text{a=random(-1,1)>0?\a:(-\a)}
\text{sum=1 + \a + \a^2 + \a^3 + ... + \a^n}
\text{sum=\inverse=1?1/(\sum)}
\real{lim=\inverse=0?1/(1-\a):(1-\a)}
\real{lim=\big=1?0}

\statement{Calcular el límite de la sucesión (<i>u<sub>n</sub></i>), donde
<p><center>
\( u_n = \sum )
</center> <p>
}

\answer{lim(<i>u<sub>n</sub></i>)}{\lim}{type=numeric}

\hint{One might use the formula
<p><center>
\( 1+x+x^2+...+x^n = (1-x^(n+1))/(1-x) ) .
</center> <p>
}
