  The cosmographic approach is adopted to determine the spatial curvature
(i.e., $\Omega_K$) combining the latest released cosmic chronometers data (CC),
the Pantheon sample of type Ia supernovae observations, and the baryon acoustic
oscillation measurements. We use the expanded transverse comoving distance
$D_M(z)$ as a basic function for deriving $H(z)$ and the other cosmic
distances. In this scenario, $\Omega_K$ can be constrained only by CC data. To
overcome the convergence issues at high-redshift domains, two methods are
applied: the Pad\'{e} approximants and the Taylor series in terms of the new
redshift $y=z/(1+z)$. Adopting the Bayesian evidence, we find that there is
positive evidence for the Pad\'{e} approximant up to order ($2,2$) and weak
evidence for the Taylor series up to 3-rd order against
$\Lambda\text{CDM}+\Omega_K$ model. The constraint results show that a closed
universe is preferred by the present observations under all the approximants
used in this study. And the tension level of the Hubble constant $H_0$ is less
than $2\sigma$ significance between different approximants and the local
distance ladder determination. For each assumed approximant, $H_0$ is
anti-correlated with $\Omega_K$ and the sound horizon at the end of the
radiation drag epoch, which indicates that the $H_0$ tension problem can be
slightly relaxed by introducing $\Omega_K$ or any new physics which can reduce
the sound horizon in the early universe.
