Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Probabilitas dan Statistika |
Periode Ujian |
: |
Mei 2018 |
Nomor Soal |
: |
6 |
SOAL
\(\mathop {\lim }\limits_{n \to \infty } \frac{{{5^n}}}{{n!}} = \)
- 0
- \(\frac{1}{2}\)
- 5 ln 5
- \(+ \infty \)
- Tidak ada jawaban yang benar
Step 1 |
\(\mathop {\lim }\limits_{n \to \infty } \left. {\left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right.} \right| = L\)
\(\mathop {\lim }\limits_{n \to \infty } \left. {\left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right.} \right| = \mathop {\lim }\limits_{n \to \infty } \left. {\left| {\frac{{\frac{{{5^{n + 1}}}}{{n + 1!}}}}{{\frac{{{5^n}}}{{n!}}}}} \right.} \right|\)
\(\mathop {\lim }\limits_{n \to \infty } \left. {\left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right.} \right| = \mathop {\lim }\limits_{n \to \infty } \left. {\left| {\frac{5}{{n + 1}}} \right.} \right|\)
\(\mathop {\lim }\limits_{n \to \infty } \left. {\left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right.} \right| = \frac{1}{\infty } = 0\) |
Maka |
L < 0 yaitu memiliki sifat konvergen sehingga \(\mathop {\lim }\limits_{n \to \infty } \frac{{{5^n}}}{{n!}} = 0\) |
Jawaban |
a. 0 |