Math Problem Solver

$$\frac{1}{9} + \frac{1}{6561} + \frac{1}{729} + \frac{1}{81} = \frac{820}{6561} \approx 0.12498094802621551592745008382868$$

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of $\frac{1}{9}$, $\frac{1}{6561}$, $\frac{1}{729}$, and $\frac{1}{81}$ is $6561$. $$\begin{aligned} \frac{1}{9} + \frac{1}{6561} + \frac{1}{729} + \frac{1}{81} &= \frac{1 \cdot 729}{9 \cdot 729} + \frac{1 \cdot 1}{6561 \cdot 1} + \frac{1 \cdot 9}{729 \cdot 9} + \frac{1 \cdot 81}{81 \cdot 81} \\ &= \frac{729 + 1 + 9 + 81}{6561} \\ &= \frac{820}{6561} \end{aligned}$$