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

Let's start by analyzing the given function and solving the problems step by step.

### Function Analysis

The given function is:
\[ f(x) = \sin^2(x) + \sin(x) + \cos^2(x) \]

First, simplify the function:
\[ \cos^2(x

Explore the function f(x) = sin^2(x) + sin(x) + cos^2(x) and solve specific problems related to its symmetry center and the number of zeroes on the interval [0, nπ/2]. Gain insights into trigonometric identities and function analysis suitable for high school students.

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