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.

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