# Nakafa Framework: LLM

URL: https://nakafa.com/id/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/15

Exercises: Try Out - Set 8: Simulasi ujian nyata untuk mengasah kemampuan dan kepercayaan diri. - Soal 15

---

## Exercise 15

### Question

export const metadata = {
  title: "Soal 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Jika diketahui bahwa

<BlockMath math="x = \frac{1}{2015} - \frac{2}{2015} + \frac{3}{2015} - \frac{4}{2015} + \dots - \frac{2014}{2015}" />

Maka nilai <InlineMath math="x" /> yang memenuhi adalah...


### Choices

- [x] $$-\frac{1007}{2015}$$
- [ ] $$-\frac{1008}{2015}$$
- [ ] $$\frac{1}{2015}$$
- [ ] $$\frac{1007}{2015}$$
- [ ] $$\frac{1008}{2015}$$

### Answer & Explanation

export const metadata = {
  title: "Pembahasan Soal 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Dalam operasi hitung penjumlahan atau pengurangan, bisa menggunakan sifat asosiatif untuk mempermudah penghitungan.

<BlockMath math="\begin{aligned} x &= \frac{1}{2015} - \frac{2}{2015} + \frac{3}{2015} - \frac{4}{2015} + \dots - \frac{2014}{2015} \\ &= \left(\frac{1}{2015} - \frac{2}{2015}\right) + \left(\frac{3}{2015} - \frac{4}{2015}\right) + \dots + \left(\frac{2013}{2015} - \frac{2014}{2015}\right) \\ &= \left(-\frac{1}{2015}\right) + \left(-\frac{1}{2015}\right) + \dots + \left(-\frac{1}{2015}\right) \end{aligned}" />

Terdapat <InlineMath math="\frac{2014}{2} = 1007" /> kelompok, sehingga:

<BlockMath math="x = -\frac{1}{2015} (1007) = -\frac{1007}{2015}" />


---