One small mistake and lo behold

Take a look at the thin rod(of length $a$ ) above.

The mass density along the rod varies as $\sigma=\sigma_{0}(1+\frac{x^{n}}{a^{n}})$ where $n$ is a positive integer.

While calculating the co-ordinates of the centre of mass of the rod, we assume(wrongly) the COM to be at the geometric centre ie., $(\frac{a}{2},0)$

Now, we know that's wrong and find the actual co-ordinate.

We note that the actual $x$ co-ordinate is $\frac{a}{2}+\delta X$ where $X$ is the actual co-ordinate of the COM.

Define $100\frac{\delta X}{X}$ as percentage error

Approximately what mean maximum percentage error will we have made in assigning the COM to rods from $n=1$ to $n=20$ ie., $\displaystyle \frac{100}{20} \sum_{n=1}^{n=20} \frac{\delta X_{n}}{X_{n}}$ where $X_{n}$ is the COM when $n$ is the exponent of $x$ in the surface density expression

You may use the approximations $1 + \dfrac12 + \cdots + \dfrac1{21} \approx 3.645$ and $\dfrac1{23} + \dfrac1{24} + \dfrac1{25} \approx 0.12514$ .

Give your answer to the nearest integer.

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