Think of mediant fractions

Algebra Level 1

\[ \dfrac{7}{13} < \dfrac{7 + 1}{13 + 1} < \dfrac{7 + 2}{13 + 2} \]

The inequality above is true. Is the inequality below also true?

\[ \dfrac{7}{13} < \dfrac{7 + 1}{13 + 1} < \dfrac{7 + 2}{13 + 2} < \dfrac{7 + 3}{13 + 3} \]

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