Math Problem Solver

\[ 1 + \frac{5}{11} + \frac{9}{121} = \frac{185}{121} = 1.\overline{5289256198347107438016} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{1}\), \(\frac{5}{11}\), and \(\frac{9}{121}\) is \(121\). \[ \begin{aligned} 1 + \frac{5}{11} + \frac{9}{121} &= \frac{1 \cdot 121}{1 \cdot 121} + \frac{5 \cdot 11}{11 \cdot 11} + \frac{9 \cdot 1}{121 \cdot 1} \\ &= \frac{121 + 55 + 9}{121} \\ &= \frac{185}{121} \end{aligned} \]