Deret (matematika): Perbedaan antara revisi
Konten dihapus Konten ditambahkan
Baris 504:
<math>\begin{aligned} \sum\limits_{n = 1}^\infty \left|\frac{(-1)^{n+1}}{2^{n}}\right| &= \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots + \frac{1}{2^{n}} \rightarrow \text{konvergensi}\\ \sum\limits_{n = 1}^\infty \left|\frac{(-1)^{n+1}}{n}\right| &= 1 + \frac{1}{2} + \frac{1}{3} + \cdots +\frac{1}{n} \rightarrow \text{tidak konvergensi}. \end{aligned}</math>
==== Contoh 3 ====
Berapa nilai dari <math>(1 - \frac{1}{2}) \cdot (1 - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})</math>?
: <math>(1 - \frac{1}{2}) \cdot (1 - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5}) = \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} = \frac{1}{5}</math>
==== Contoh 4 ====
Berapa nilai dari <math>\frac{1}{4 \cdot 5} + \frac{1}{5 \cdot 6} + \frac{1}{6}</math>?
: <math>\frac{1}{4 \cdot 5} + \frac{1}{5 \cdot 6} + \frac{1}{6} = \frac{1}{20} + \frac{1}{30} + \frac{1}{6} = \frac{3}{60} + \frac{2}{60} + \frac{10}{60} = \frac{15}{60} = \frac{1}{4}</math>
: jadi lebih singkatnya adalah <math>\frac{1}{4 \cdot 5} + \frac{1}{5 \cdot 6} + \frac{1}{6} = \frac{1}{4}</math>
== Lihat pula ==
| |||