Math Problem Solver

\[ 1 + \frac{2}{10} + \frac{3}{100} + \frac{4}{1000} + \frac{5}{10000} = \frac{2469}{2000} = 1.2345 \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{1}\), \(\frac{2}{10}\), \(\frac{3}{100}\), \(\frac{4}{1000}\), and \(\frac{5}{10000}\) is \(10000\). \[ \begin{aligned} 1 + \frac{2}{10} + \frac{3}{100} + \frac{4}{1000} + \frac{5}{10000} &= \frac{1 \cdot 10000}{1 \cdot 10000} + \frac{2 \cdot 1000}{10 \cdot 1000} + \frac{3 \cdot 100}{100 \cdot 100} + \frac{4 \cdot 10}{1000 \cdot 10} + \frac{5 \cdot 1}{10000 \cdot 1} \\ &= \frac{10000 + 2000 + 300 + 40 + 5}{10000} \\ &= \frac{12345}{10000} \\&= \frac{2469}{2000} \end{aligned} \]