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 |
