Algebra · Geometric series · Decimal expansions · Monotonicity · Fraction comparison
Problem 4, 2006
← Prev · 22 / 22 · Next →Which of the following two numbers is greater:
\[ \frac{1.\underbrace{11\ldots1}_{2005 \text{ digits}}}{1.\underbrace{11\ldots1}_{2006 \text{ digits}}} \qquad \text{or} \qquad \frac{1.\underbrace{0101\ldots01}_{4010 \text{ digits}}}{1.\underbrace{0101\ldots01}_{4012 \text{ digits}}} \, ? \]
In each of the four decimals the indicated digits are the digits after the decimal point.
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Serbian Regional Competition (Okruzno takmicenje) 2006, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source