# 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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