# Sum until Infinity

**Calculus**Level 4

If given that\(\displaystyle \sum_{1}^{\infty} \frac{x^{2}}{16^{x}} = \frac{a}{b}\), find the value of \[ \sqrt{a^{2}+b^{2}}.\]

**Note:** \(\frac{a}{b} \) is in the simplest ratio with no common multiples. And round off the final answer up to 3 decimal places.