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Average value of $1/(4+5+6+…)$

Consider the sequence $1,5,4,16,…$ (the fractional parts of $\pi$) and the average value of the sequence. Can anyone help me find this value?
I am totally confused.
Thank you.

A:

$$\frac{1}{4} + \frac{5}{16}+\frac{4}{16} +\ldots=\frac{5}{4}$$

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