Sum that Equals to One

$\small \begin{aligned} \sum_{n=2}^\infty \frac{1}{n^{1.7}} ≈ 1.05429 & > 1 > \sum_{n=2}^\infty \frac{1}{n^{1.8}} ≈ 0.88223 \\ \sum_{n=2}^\infty \frac{1}{n^{1.72}} ≈ 1.01592 & > 1 > \sum_{n=2}^\infty \frac{1}{n^{1.73}} ≈ 0.99755 \\ \sum_{n=2}^\infty \frac{1}{n^{1.728}} ≈ 1.00118 & > 1 > \sum_{n=2}^\infty \frac{1}{n^{1.729}} ≈ 0.99936 \\ \sum_{n=2}^\infty \frac{1}{n^{1.7286}} ≈ 1.00009 & > 1 > \sum_{n=2}^\infty \frac{1}{n^{1.7287}} ≈ 0.9999 \end{aligned}$

The value of $x$ is $\approx 1.7286$ or $\boxed{1.729}$ .