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


Răspuns :


[tex]lim \: \frac{qn + 1}{qn} \times \frac{qn + p + 1}{qn + p} \times ... \times q \\ \frac{qn + np + 1}{qn + np} [/tex]
[tex]lim \: \frac{qn + 1}{qn} \times lim\frac{qn + p + 1}{qn + p} \times ... \times q \\lim \frac{qn + np + 1}{qn + np} [/tex]