$$ 17\text{. (}15分)\text{ 已知函数}f\left(x\right)=\sin^2x+\sin x+\cos^2x\text{.} $$
$$ \text{(}1)\left(6分\right)求函数f\left(x\right)的对称中心\text{.} $$
$$ \left(2\right)\left(9分\right)\,若函数f\left(x\right)在区间\left\lbrack0,\text{ }\frac{n\pi}{2}\right\rbrack上恰好有2024个零点\text{, 求实数}n的取值范围\text{.} $$

Given the function $ f(x) = \sin^2 x + \sin x + \cos^2 x $, we will address both parts of the problem sequentially.

### Part (1) Find the Symmetry Center of the Function $ f(x) $

First, simplify the function $ f(x) $:

\[
f(x) = \sin^2 x + \sin x + \cos^2 x
\]

Using the Pythagorean identity, $\sin^2 x + \cos^2 x = 1$:

\[
f(x) = 1 + \sin x
\]

This function is linear in terms of $\sin x$, and we can analyze its symmetry properties. To check if it has any symmetry center, we

Explore the function f(x) = sin^2 x + sin x + cos^2 x and solve for its symmetry center and the range of n where it has 2024 zero points within the interval [0, nπ/2]. Understand the application of trigonometric identities and functions in determining the behavior of f(x).

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