Question

Limita când n tinde la infinit:
$lim \: \frac{qn + 1}{qn} \times \frac{qn + p + 1}{qn + p} \times ... \times q \\ \frac{qn + np + 1}{qn + np}$
A)
$\sqrt[p]{ \frac{p}{q} }$
B)
$\sqrt[p]{ \frac{p + q}{q} }$
C)
$\sqrt[p]{\frac{q}{p + q} }$
D)
$p \times \sqrt[p]{ \frac{p}{q} }$
E)
${p}^{2} \times \sqrt[p]{ \frac{p}{q} }$
La răspunsuri spune ca este B) (culegere admitere UTCN)

Answer 1

$lim \: \frac{qn + 1}{qn} \times \frac{qn + p + 1}{qn + p} \times ... \times q \\ \frac{qn + np + 1}{qn + np}$
$lim \: \frac{qn + 1}{qn} \times lim\frac{qn + p + 1}{qn + p} \times ... \times q \\lim \frac{qn + np + 1}{qn + np}$