# Nakafa Framework: LLM

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

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 15

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## Exercise 15

### Question

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

Given that

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

The value of <InlineMath math="x" /> that satisfies the equation is...


### Choices

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

### Answer & Explanation

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

In addition or subtraction operations, we can use the associative property to simplify the calculation.

<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}" />

There are <InlineMath math="\frac{2014}{2} = 1007" /> groups, so:

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


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